Upvote:3
No, immigration doesn't care.
When you take medical services in the US, you are taking them from a doctor or hospital, which is either a private person or business, or a non-profit charity. With rare exception, they are not run by the US government. Whoever they are, they bill you for the medical care, at "retail" (rich foreigner) rates. That varies between "perfectly reasonable" (doctor) to "insane" ($15,000 for a $400 dialysis treatment). To be honest, they don't expect the bill to be paid in full, and it can often be settled for far less. (if you paid $400 on that dialysis bill, they're happy).
All that to say, it's a very different situation than, say, the United Kingdom; where the government (NHS) pays for all healthcare and that can influence immigration.
It is certainly a doctrine of the US government that we don't want you coming to our country and flinging yourself onto public services like welfare or food stamps. But since healthcare is largely in private hands, the government will not know or care about a hospital bill outstanding from private parties.