If you go to the hospital for a real emergency and it's a life and death situation then no the hospital cannot refuse you any treatment or services for unpaid medical bills.
If it's not an emergency then the hospital may be able to turn you away but most will not turn you away because they could get a lawsuit against them if something happens.
So if you have unpaid medical bills and need to go to the emergency room for treatment then go ahead and go because they cannot refuse service and they will still treat you even if you haven't paid them any money.
You also can can go to the hospital even without health insurance or the money to pay for the emergency room visit.
If it's not an emergency it's best to go to the doctor when you can but if it's an emergency then you should go to the emergency room.