no, it wouldn't. if a person cannot afford treatment at the er, they can always make payment arrangements. it's against the law for the er to refuse treatment to anyone. besides, a hospital would rather accept $20/month as payment for their services instead of nothing at all. aside from that, a hospital cannot prove someone isn't an indigent since they have no access to their personal assets or insurance records if that individual doesn't provide an insurance card. if a hospital requests a social security number, a person can always lie and say they don't have one.
That would be fraud and could land the person in jail. Plus the government now requires SSN at a very early age so that would not be believed.