1) Europe didn't made America more civilized, it just turned it european. Not in the most civilized manner.
2) Zheng He didn't discovered America, from what we know at least. The main proponent of this theory is a loony and his thesis are a joke.
3) Siam was more interested on Indian Ocean and Indonesian seas at this moment, and really gained regional hegemont with its main rival, Malacca, being taken by Portuguese. It doesn't help it went into pressure from Burma at the same period.
Maybe if Zheng He decides to act stupid and crush Malacca during his trips, you could end with Siam having a more important naval domination on the region, and by a really far-fetched move, decides for the lulz of it to go eastwards.
I don't think you'd had the focus, the ressources and the strategical possibilities to pull a Cortez on America, though : Pacific is freaking huge, ask for more important ressources to cross, and doing so because "hey why not", seems a bit...well, weird.
Not that a South-East Asian expedition in Americas is unthinkable, but Siam doesn't seem to be the best placed for that, at least in the XVth century. Majapahit Empire, for instance, seems a more likely candidate.