It depends on the psychiatrist. In the United States most psychiatrists really only deal with med management but this is largely a situation that has been created by insurance companies. Insurance companies don't want to pay for longer therapy appointments with a psychiatrist when you can get therapy from a less expensive psychologist or therapist. There are psychiatrists who also do their own therapy but in my experience they usually don't accept insurance and the patient must pay private, out of pocket fees. Depending on your insurance plan, you may be able to submit receipts to the insurance company for partial reimbursement but it won't come close to what you actually paid.
The specific numbers escape me at the moment, but I recently read some studies that showed the alarmingly increasing number of psychiatrists who do not accept insurance for a variety of reasons. The percentage of psychiatrists who do no accept any form of insurance is higher than any other medical specialist.