yes sure you can come into america, straight into a holding cell until you hand over your pins/passwords or go back home.
Unlikely, but if that did happen an army of lawyers would be willing to help pro bono for such a constitutionally critical case.
Never comply with such nonsense.
You are seriously inconvenienced, but assuming your paperwork is in order, you will be allowed into the US. This isn't just against US law, it's a violation of international law to render a person stateless.
This ignores the real point, which is that while you cannot be refused entry to the United States, you can be arrested at the border. ICE these days has mastered the art of making people's detainment so uncomfortable that even those with a right to be in this country end up deciding to leave.