It depends why you are splitting up and how you get on generally. I speak from bitter and recent experience. I have just split with my partner and he is moving out in the next few months: still hasn't decided what to do or where he wants to live.
Previous to this decision (which felt very inevitable) we had thought we could just go on living in the same house for DS's sake. But we just argue ALL the time and it began to feel like a living hell. WE both felt unhappy. So now one of us has to move out.
In the past, after I split with my first boyfriend, he stayed for another 4 months, dragging his heels probably in hope of a reconciliation.. That was a very bad plan because it really soured things between us and we ended up enemies which is sad.. Remember that sharing a home with anyone is hard, even if you love them. If you've just split up, you're not going to be feeling too friendly and tempers will be strained.
I do sympathize with your situation. For us it is more money worries and the cost of him renting another place while simultaneously wanting to leave his job because he hates it. But still, it sounds like you two are considering staying in the same house for the same reason we were: because he is scared. I know mine is scared of moving out and what he will do, and I have major guilt for being part of that, I feel I have partly caused it. It's very difficult to be tough and say, look, you NEED to go, but sometimes you have to say it and save yourself a lot of pain and arguing. Has your XP got any other support? He obviously has his therapist. It sounds like he is stalling and hopes that if he ignores the problem, it will somehow go away. Thus, your idea of slowly slowly easing him into a new life and new place may not work, because he has his head firmly in the sand. He doesn't want to move out by degrees, at a pace that's right for him - he just doesn't want to go at all. At least that's what it sounds like.
Anyway, sorry for the marathon reply. I hope you find a solution that works for you all, but don't neglect your needs and mental heath also in this process. The right answer is one in which both people are being considered, not just him. And in answer to your original question, yes it can work but not always for very long, and most people would probably advice against it. Clean break and all that