Does this even work? Will they even treat you or let you leave without ID?
I wonder about that too. Perhaps if it is severe enough?

They must get you to be “stable” legally.

That doesn’t mean healthy or cured.

You will still have a bullet in you. Your bone will still be broken. You will still have that cyst.

Also doesn’t mean they will prioritize your entry. Your ass could die in the waiting room while they decide what to do with you.