To have Polish ancestors doesn't make you a Pole.
Over here, it appears that if you are second-generation, you stop being <insert ethnicity here>, but only if you are white.
If, for example, you are Pakistani, then you're still a "Paki" even after three or four generations.
Unless you're a sportsman, of course :D
If you run the local corner shop and speak with an "accent", then you get called a "Paki shop owner", but if you're an "Asian" boxer from Bolton, you get called "British" even if you wave both the Pakistani and Union flags after winning a fight. There's clearly a degree of hypocrisy within UK society ;)
But it could be worse - my sister only calls herself Polish if she gets passed over for promotion at work, and tries to plan an ethnic "race card" - it's hilarious to hear about it, because the rest of the time she talks about how "east Europeans" should "**** off back home and stop taking all the benefits"! :D Needless to say, she speaks no Polish.
I, on the other hand, have spoken excellent Polish all my life, married a 2nd generation Pole in a Polish church, and have been in several other relationships with Polish women (one actually from Poland, who spoke virtually no English), totalling around 13-14 years.
I have minimal contact with non-family Poles now though, because I don't like the attitude of most of those who have come over since 2004 (there is a degree of "generation gap" here, but it goes beyond that - but that's beyond the scope of this post, and I'm not willing to elaborate for personal reasons).
So I would say that I'm entitled to call myself Polish, but unlike
some (bold text for the benefit of p3undone ;) ) of the Pol-Ams on here, I never mention it unless someone else does, or someone sees my surname and comments on it.
I can guarantee that you would never, ever see me driving around with some "Yeehaa! Damn right I'm Polish!!" car sticker like some Poland-avoiding, non-Polish speaking Polish-American probably would.