I think it would be very hard in modern times. In every state, you have to have a license to practice medicine. The state board, which issues the licenses, checks qualifications carefully, including I.D. and transcripts. Hospitals, clinics, etc. would check the license before hiring a doctor.
I guess you might get away with not having a license in a private practice, but I suspect not for very long.
The only way I can figure for this to happen in modern times is identity theft. If Joe Schmoe is a doctor, and you steal his identity, then his credentials would check out and you might be successful. At least for a time.