Wow, you have your plate full already. Does he want to get married? Does he think he is capable of fulfulling his role as partner, support, lover, etc? Do you think he is?
If he doesn't want to go to therapy, it may seem he's not wanting to take any responsibility. Of course, who would....it's a lot of work.
Living with a person with anxiety, depression and "issues" is difficult, especially when one has baggage from family, etc. My husband can attest to that. But, we've worked on things together, as well as me doing therapy, cognitive behavioural therapy, biofeedback and meds now for depression (Effexor XR). I'm not even in the ballpark of psych meds as your fiance is, but I do have other health disorders to deal with and meds for them as well. We've been together 25 years, no kids because of hereditery, meds and my probable inability to cope with the daily grind of dealing with them. But, it was a conscious decision that hasn't hurt our relationship at all. We've never regretted that.
Now for you......I'd walk, it seems his issues are way beyond what you should have to deal with. Just ask yourself if you are with him out of love, out of pity, or that you can't or deserve anyone who will be an equal partner in the relationship.
It's different when things happen when in a marriage, partners are/should be well established and commited even before marriage. But, you have your slate already written out for you. It's as good as you'll get in telling your future.
I wish you the best, no matter your decision.
Best to you,
quincy