i fail to see how "democracy" has anything to do with this. it's all about land and territorial claim. i mean if an inland chinese province suddenly declares independence and calls itself a democracy, would any one try to support it militarily? china sees taiwan as a part of itself, and there is a 100% chance of invasion if taiwan is stupid enough to declare independence.
the US also has a clever escape clause. it opposes "unilateral action on either side". so if taiwan just declares independence, the US can say "that's unilateral action, we will not support it"
also it will be suicide for the US fleet to get involved. there are more than enough chinese cruise missiles to sink the entire 7th fleet, as pentagon's own military simulations have shown before