No.  In practices offering concierge care, patients typically pay a high retainer fee in addition to insurance premiums and other plan obligations (e.g., copays, out-of-pocket expenditures), and the practice continues to bill the patient’s insurance carrier.
In addition, concierge care still requires the physician to restrict care based on oppressive insurance and Medicare rules, and still burdens the physician with hours and hours of paperwork, taking away time and energy better devoted to the patient.