I'll be honest and say I don't know. I think you can have hallucinations as a symptom independent of psychosis. So like if you have simple hallucinations like spots or auras or something I don't think those automatically count as psychosis but once you get up to something complex like a person or an animal I think it counts right away but I think implied in the definition of psychosis is the inability to distinguish reality from your hallucination at least initially so if you saw a cat walk up to you you might try to pet it until realizing it wasn't really there. The thing is this gets complicated because you might later realize its the same cat and therefore not real or you might realize that there probably isn't a dragon hovering 6 inches from your face---so some of that aspect is gone later.

As far as reduced functioning as far as I can tell that's primarily social and occupational so do you have friends and can you do your work or school work...my understanding is if you can do both of those things to full capacity your don't have impairment and therefore have no mental illness.