Can pseudoparkinson be treated with cogentin (benztropine)?

Depends: The severity and extent of parkinsonian symptoms, assuming what's being referred to is via other medications, will respond differently to different approaches. Some aspects may respond well (e.g. akathisia) and others not so much (e.g. dystonia) if using those drugs used to treat Parkinson Disease. Suggest a discussion with your doctor to assess what are the targets for therapy and side effects.