Yes, unless it is an emergency. Nobody can force you to do business with someone you don’t want to do business with, unless you’re trying to discriminate against a protected class. Debtors are not a protected class. So yes, doctors can refuse to see you for routine or pre-planned services if you have not paid them. Likewise, dentists and veterinarians can hold your puppies and gums hostage to their demands for money.
The big exception to this rule is for medical emergencies. If you’re shot and rushed to an ER at a hospital that you owe money to, they have to treat you. This is why so many poor people go to the ER. They don’t have health insurance or money to pay a normal doctor, so when they get sick, they just wait until it gets bad enough and becomes an emergency and then they go to the ER.
There is another, smaller exception: they cannot withhold your medical records for nonpayment of bills. They can charge you a small fee for printing copies of your records, but that’s all they can charge you. So here’s an example:
Susannah is a cancer survivor, but her insurance hit a lifetime maximum in 2011, and she had to file bankruptcy in 2012 because her medical bills were over $200,000. She still owes Greedy Oncology, PC $2,000, and she needs to see another oncologist for a follow up appointment. She found someone who will see her, but she needs the records from Greedy Oncology. The regular fee for her records is $15. When Susannah asks for her records, they can charge her $15 to provide the records, but they cannot charge her $2015, or anything beyond $15.