No an emergency room cannot legally turn you away even when you have no money, no medical insurance, health insurance etc.
The emergency room must accept you into the emergency room and treat any injuries or illnesses you have and then later they can setup payment arrangements with you.
But the emergency room will take you in when they can and treat you and diagnose any illnesses or fix any injuries you have.
The hospital may admit you to the hospital or they may discharge you that same day depending on the severity of the injuries or illness.
So if you think you need an ambulance or need to go to the emergency room then you should and worry about the bills later on.
Not everyone can pay for the emergency room bills or ambulance but if you can pay some do so but don't worry if you cannot pay all of it.
If you need the ambulance services again or emergency room treatment again you cannot be refused service even when you have medical bills you owe.