It's safe to assume that any psyche drugs they'd give her would be ineffective, correct? Or is there something that can suppress her immune system so that said medications will work on her? I'm asking because I figured at one point or another being locked in an insane asylum would result in medication and other forms of therapy being used.

My point exactly, she's supposed to be invulnerable to chemical stuff.

http://www.comicvine.com/poison-ivy/29-1697/chemical-implants/92-388691/

Poison Ivy has a hyperactive immune system that makes her immune to all diseases and gives a tolerance to all drugs. This hyper active immune system also makes it impossible to bear chilldren, let alone be impregnated 

Immune to everything, it's mentioned in Gotham City Sirens issue #5 or #6.

Could you explain further?  I understand medication, diseases, and the like, yet she has been threatened by herbicide that would, "most certainly have killed [Ivy]" (Detective Comics #751 & #752)  Where is the chemical line drawn?

" Could you explain further?  I understand medication, diseases, and the like, yet she has been threatened by herbicide that would, "most certainly have killed [Ivy]" (Detective Comics #751 & #752)  Where is the chemical line drawn? "