Without knowing all the details, it's hard to say. But, in general, they probably could. However, the agent might adopt liability if by so removing you he knowingly endangers your physical well-being.
Keep in mind that a parolee does not have aright to just go about admitting himself where he pleases while on the run. The parole agent is very likely to retrieve you and enter you into whatever medical facility your state operates for the treatment of your condition.
A mental health facility or hospital is not "home base" in a game of tag.
- Carl