No. A person appointing an agent must be mentally and legally competent to appoint an agent. Otherwise, the appointment is voidable.  Also, someone who had been declared NCM (i.e., mentally incompetent) by a Court cannot appoint an agent.

You might consider having a guardian or conservator appointed on behalf of your father.

A guardianship or conservatorship is a legal relationship between a competent adult or “guardian” and a person who is no longer able to make his own responsible decisions or “ward.” such as the legal guardianship of a minor child. The legal guardianship is appointed by a court and can be authorized to make legal, financial, and health care decisions for the ward. The guardian must regularly report to the court and may be removed if he or she does not adequately take care of the ward and adhere to the guardianship law, and conservatorship law regulations.