Of all the players in Major League Baseball, one might think that Japanese-born players are the least likely to have any connection to Judaism. There was never any significant Jewish presence on the islands of Japan (in contrast to territories occupied by Japan at various stages, especially during WWII). One could be forgiven for not anticipating a Danny Valencia situation - Cuban father, Jewish mother (go O's). So what are the chances that a player - especially Osaka-born Cy Young favorite like Yu Darvish - might have Jewish roots?
Well it turns out that there might be a chance. Yu Darvish's father is Iranian (which is not surprising if you think about it; dervishes - and that's what the name means - are from the Muslim world). He left Iran in 1977, just before the Revolution. And Alan Brill just posted the portrait of two Teherani Jewish Sufis named Darvish (here's an undated photo of Jewish Darvish family in Teheran).
Before we get carried away, Darvish is a common name among Sufis, Jewish or not. The American analogue might be something like Davis: not uncommon as a Jewish name, but also a pretty common name among gentiles. So Ike is Jewish, but, alas, Crush is not. Besides, if he does not identify as Jewish, then even the patrilinealists would concede that any Jewish roots would be a mere curiosity.
Still might be fun to look into, though.