I have never had psychosis and while I am prescribed medical cannabis and it has replaced mulitple medications (ie. Opioids, NSAIDs, bronchodialators, as well as benzos for the most part) I am still on plenty of other medications.
It has had no effect on my complaince of any of my medications though I am generally the person who is in primary control of my medications and my doctors just for the most part follow my lead and prescribe me what I ask for. I am a highly informed patient and often know more about the medications than my doctors do. Rarely do they tell me something I don't already know and often they learn bits and pieces of information about meds and available treatment options from me that they weren't aware of.