I'm not sure if I would go quite that far. It could be racist, but as it is used today, I would argue that the idea of discovering America is more an unconscious idea which seeped into a lot of people's historical mindsets. IMO it is really only racist if it is being used to directly promote some nationalist agenda.
Even ignoring the native americans (something done all to often in these discussions), there are a huge number of people who (might have) made it to the Americas. Personally, I've never really bought into the idea that the romans made it to America (although, interestingly enough, there is some evidence of contact going the other direction during that time period), but there is at least some sort of evidence which could show contact by Polynesians, Phonecians, Celtic cultures, West Africans, medieval europeans, and other groups with the americas (in fact, contact may never have stopped between Siberia and Alaska). In a way, the whole discussion is moot; the most important discoverer is the last one, because that is the guy that the historians remember.
As for the original question, no, Zheng he did not make it to America, whatever Gavin Menzies wants to think.