No, not typically. It's a fellowship to allow for more training to use in treatment of Behavioral health in the outpatient setting.
To be an attending/staff in an inpatient psychiatric unit, you'd need psychiatric residency. You could try applying sequentially for a psychiatric residency after completing FM, or if you are still in med school, you could apply for the FM-psych combined programs.
Outpatient psych mostly But you get a lot more comfortable managing antidepressants and antipsychotics
Also you hone your psych interview skills
Even then I would recommend it’s always best to have a back up psychiatrist for the very difficult cases. I would not market myself as a psychiatrist by any means even after such a fellowship,