First I had to come up with a list of players. I started with the list of MLB players born in Japan from Baseball Reference. I then removed anyone from the list who did not play in NPB prior to playing in MLB - so good bye to the Westerners who were born in Japan (like Jim Bowie & Dave Roberts) and Japanese players who signed with US teams instead of NPB teams (like Junichi Tazawa, Mac Suzuki and Michael Nakamura). That gave me a list of 47 players. I dropped Masanori Murakami from the list as his US career was before the modern card era in Japan. I then added a couple other players who weren't on the list - Hiroyuki Nakajima (only played in Oakland's farm system in 2013), Tsuyoshi Wada (only played in Baltimore's farm system in 2013), Wei-Yin Chen (born in Taiwan but started career in NPB) and Chang-Yong Lim (born in Korea but started career in NPB) for a total of 50 players. I think this pretty much hits everyone who went from NPB to "organized ball" in North America in the last 20 years.
The list is Norichika Aoki, Wei-Yin Chen, Yu Darvish, Kyuji Fujikawa, Kosuke Fukudome, Kazuo Fukumori, Shigetoshi Hasegawa, Ryota Igarashi, Kei Igawa, Tadahito Iguchi, Hideki Irabu, Kazuhisa Ishii, Hisashi Iwakuma, Akinori Iwamura, Kenji Johjima, Takashi Kashiwada, Kenshin Kawakami, Munenori Kawasaki, Masao Kida, Masahide Kobayashi, Satoru Komiyama, Hiroki Kuroda, Masumi Kuwata, Chang-Yong Lim, Hideki Matsui, Kazuo Matsui, Daisuke Matsuzaka, Hiroyuki Nakajima, Norihiro Nakamura, Tsuyoshi Nishioka, Hideo Nomo, Takahito Nomura, Tomo Ohka, Hideki Okajima, Akinori Ohtsuka, Takashi Saitoh, Kazuhiro Sasaki, Tsuyoshi Shinjo, Ichiro Suzuki, So Taguchi, Hisanoari Takahashi, Ken Takahashi, Shingo Takatsu, Kensuke Tanaka, Yoshinori Tateyama, Koji Uehara, Tsuyoshi Wada, Keiichi Yabu, Yasuhiko Yabuta and Masato Yoshii.
Once I had a list, I started looking at the cards these players had (if any) during their time in the US. As it turned out, there were actually quite a few of these cards. Now I need to stop here and point out that I looked mostly at what I have in my collection. I have a lot of cards but I don't have everything - I don't have much Calbee from between 1990 and 2011 and I don't have many of BBM's team sets. I only have partial BBM flagship sets from 1994-2000 and only partial sets of the "Historic Collection" sets from 2003-2006. So this may skew my results somewhat.
The cards I found were all BBM cards. As I said, my pre-2012 Calbee is a bit sparse but I do know that there's a couple of times in both the 2012 and 2013 sets where it would have been appropriate for Calbee to have a card of an MLB player but they failed to do so.
For the most part the cards I found can be divided into two categories - flagship set cards and OB set cards. The flagship set cards are the "Leader" subset cards from the BBM flagship sets as well as Best 9 and Golden Glove insert set or subsets and Highlight/Record Breaker cards. The OB set cards are cards for the player in one of BBM's historic sets, be it the annual "Historic Collection" sets or a team-based OB set (as well as the historic focused sets that don't fall into either of these categories).
For an example of the "flagship" cards would be for Ichiro Suzuki. In 2000, Ichiro's final season in Japan, he lead the Pacific League in batting and OBP as well as making the Best 9 and Golden Glove teams. He has cards in the 2001 BBM set's league leader subset and the Best 9 and Golden Glove insert sets, despite spending 2001 in the US playing for the Mariners. At least
The earliest occurrence of an MLB player having a card in the flagship set is 2001 but something similar happened earlier. Jim Traber of the Kintetsu Buffaloes lead the Pacific League in RBIs in 1991 but he did not return to Japan for 1992. He had a card in the 1992 BBM set's leader subset however, despite not having a "regular" card in the set (since he was no longer in NPB). I can't swear that this did not happen any other times in the 1990's but I have not found any other examples.
There's three different types of OB sets that the MLB players have appeared in - the annual "Historic Collection" sets, the team based OB sets and the (for lack of a better term) "special" OB sets - the 2000 20th Century Best 9, the 2009 Legend Players and the 2010 BBM 20th Anniversary sets. 36 of the 50 players have appeared in at least one of these sets - Norichika Aoki (2013 Great Numbers), Kyuji Fujikawa (2013 Great Numbers*), Kosuke Fukudome (2010 BBM 20th, 2011 Dragons 75th, 2011 Hometown Heroes), Kazuo Fukumori (2008 Back To the 70's*), Ryota Igarashi (2010 Memory Makers*, 2010 BBM 20th), Kei Igawa (2007 Draft Story*, 2010 BBM 20th, 2010 Tigers 75th, 2011 Hometown Heroes), Tadahito Iguchi (2008 Hawks 70th), Kazuhisa Ishii (2002 All Time Heroes*), Hisashi Iwakuma (2013 Great Numbers), Akinori Iwamura (2007 Draft Story*, 2009 Yakult 40th, 2010 BBM 20th), Kenji Johjima (2007 Draft Story, 2008 Hawks 70th, 2009 Legend Players), Kenshin Kawakami (2010 BBM 20th, 2011 Dragons 75th, 2011 Hometown Heroes, 2011 Legend Of Tokyo Big Six), Munenori Kawasaki (2013 Hawks 75th, 2013 Fukuoka Legacy), Masahide Kobayashi (2008 Lotte 40th), Hiroki Kuroda (2008 Back To The 70's*, 2008 Hiroshima Memorial, 2009 Hiroshima 60th, 2010 BBM 20th, 2011 Tohto 80th Memorial, 2013 Great Numbers), Masumi Kuwata (2007 Draft Story*), Chang-Yong Lim (2013 Deep Impact), Hideki Matsui (2003 Sluggers*, 2004 Giants 70th, 2007 Draft Story, 2007 HR Chronicle, 2009 Legend Players, 2010 BBM 20th, 2011 Hometown Heroes, 2012 Greatest Games #1), Kazuo Matsui (2008 Seibu 30th, 2009 Legend Players, 2010 BBM 20th , 2010 Lions 60th), Daisuke Matsuzaka (2007 Draft Story*, 2007 Leaders, 2009 Legend Players, 2010 Lions 60th), Hiroyuki Nakajima (2013 Great Numbers*), Tsuyoshi Nishioka (2011 Hometown Heroes*, 2011 Marines 20th), Hideo Nomo (2000 20th Century Best 9), Hideki Okajima (2013 Giants Legend*, 2013 Hokkaido 10th), Takashi Saitoh (2008 Baystars 30th, 2010 BBM 20th), Kazuhiro Sasaki (2000 20th Century Best 9), Ichiro Suzuki (2007 Draft Story, 2009 Legend Players, 2009 Orix 20th), So Taguchi (2002 All Time Heroes*, 2009 Orix 20th), Hisanori Takahashi (2011 Tohto 80th, 2013 Giants Legend), Ken Takahashi (2009 Carp 60th), Kensuke Tanaka (2013 Leader, 2013 Great Numbers*, 2013 Hokkaido 10th), Yoshinori Tateyama (2013 Hokkaido 10th), Koji Uehara (2010 BBM 20th, 2013 Giants Legend), Tsuyoshi Wada (2012 Strongest Generation*, 2013 Great Numbers, 2013 Hawks 75th, 2013 Fukuoka Legacy), Keiichi Yabu (2005 Tigers 70th) and Yasuhiko Yabuta (2008 Lotte 40th).
Some of the sets I listed above came out very early in the year they are listed in (or actually came out the previous year) and may have gone to press before the player announced they were going to the US. For example, the "Draft Story" set has a "cover date" of 2007 but it was released in November of 2006 (and probably went to press in October) so maybe saying it came out while Kei Igawa (who made his MLB debut in April 2007) was in MLB is pushing it a little. I've marked those sets with a "*". There's four players (Kyuji Fujikawa, Kazuo Fukumori, Kazuhisa Ishii and Masumi Kuwata) who only have one of these sets listed so maybe I should not count them.
The first BBM OB set (well actually the first BBM set at all) to feature players who were at that time playing in the US was the 2000 20th Century Best 9, which had Hideo Nomo and Kazuhiro Sasaki in it (although Nomo's cards did not actually feature his picture). The first of the annual "Historic Collection" to unequivocally include current MLB players was the 2007 Draft Story set. The first team based OB set to feature an MLB player was the 2004 Giants 70th Anniversary set (Hideki Matsui) (which was pretty much the first of those type of sets).
By my reckoning, 38 of the 50 players I listed had cards in Japan during their US stints. The 12 who didn't were Wei-Yin Chen, Yu Darvish, Shigetoshi Hasegawa, Hideki Irabu, Takashi Kashiwada, Masao Kida, Satoru Komiyama, Norihiro Nakamura, Takahito Nomura, Tomo Ohka, Akinori Ohtsuka and Masato Yoshii. Four of these players (Kashiwada, Komiyama, Nakamura and Nomura) only played abroad one season. Several of the others (Hasegawa, Irabu, Kida, Ohtsuka and Yoshii) played in the US prior to BBM including MLB players in the "Historic Collection" sets and didn't play for teams that had Anniversary sets while they were in the States. Tomo Ohka's NPB career was fairly brief. So honestly, the only ones that it's odd that they have not had cards while they've played in the US are Chen and Darvish. Chen could have easily been included in either of the gaijin sets BBM put out this year (like Lim was). Darvish, as I have mentioned in the past, should have had a leader subset card in the 2012 BBM 1st Version set as he lead the PL in strikeouts in 2011, his last year in Japan. He also could have been included in the Fighters 10 Years In Hokkaido set as the other NPB ex-patriots who were former Fighters - Tanaka, Okajima, Tateyama - were in the set.
I do not know the rhyme or reason of how BBM decides to include MLB players in the OB sets. Why is Kazuo Matsui in both the 2008 Seibu 30th Anniversary and the 2010 Lions 60th Anniversary sets but Daisuke Matsuzaka only in the latter? Why is Hideki Kuroda's #15 a "Great Number" (and warrants an appearance by Kuroda in the 2013 Great Numbers "Historic Collection" set) but Ichiro Suzuki's #51 isn't? And how does it work? Does BBM approach the player or does the player approach BBM? (I'm going to guess the former) I guess from a licensing standpoint there's no difference to BBM between getting an agreement from an active major leaguer and a retired player. My bet is neither Kyuji Fujikawa or Katsuya Nomura is party to whatever licensing agreement exists between BBM and the Japanese version of the Player's Association.
And why does Darvish not appear on a 2012 Leader subset card? The only other time I know of where someone should be on a card like that but isn't is the 2001 set, which does not have a leader subset card for the 2000 Central League hit leader or an insert card for the Central League Best 9 second baseman - in both cases it was Bobby Rose.
So to wrap up a long and somewhat winding post, it turns out that it's not that unusual for an MLB player to appear in a BBM set, although finding a predictable pattern may be difficult.