Private health insurance plans do indeed cover GP (General Practitioner) office visits. Some health insurance plans have in network copay's for doctor visits (and higher copay's for out of network visits).
If your plan does not have a doctor visit copay you will pay the negotiated rate when you use a network doctor. Your out of pocket cost for using a non-network doctor will be considerably higher.
If your plan does not have a doctor visit copay you will pay the negotiated rate when you use a network doctor. Your out of pocket cost for using a non-network doctor will be considerably higher.