Can a Doctor refuse treament if you refuse to give a copy of your Id in addition to insurance info?

Absolutely.

The doctor-patient relationship isn't established before the doctor accepts you as a patient (prior to going into an exam room). As such, the doctor has the same right not to do business with you as any other business proprietor. Only in true life threatening emergency situations (and that only in some states) is he legally obligated to provide service.

As an aside, there's a legitimate reason your doctor demands some form of legal identification. Oftentimes this ID provides the only means of tracing a patient. People using another person's insurance card (fraud) or a forged card is something that happens more than you realize.

In my practice, submitting a legal ID isn't mandatory for care. But if this is something the patient chooses, we insist on payment in full, in cash, at the time of service.