On the information you've got WQ, no I wouldn't. Obviously, I know your story and you are in a hugely vulnerable place right now. I don't think a serious relationship would be the best thing for you right now, having only recently had a marriage break-up.
Also, if I recall, you were quite insular in your marriage and didn't spend much time making and going out with friends. This is therefore the opportunity for you to enjoy singledom and reaching a peace with yourself, enjoying new friendships and being a single woman.
I think you know my stance on the issue of infidelity. I evidently don't agree that once a cheater always a cheater, but I don't have any tolerance for weak characters who wait until someone else looms into view before leaving a relationship. I think the story he has told you about his unsociable wife's behaviour leading to his "accidental" infidelity is a pile of crap tbh. He had a choice in the matter after all. Unless I had spoken to her too and heard her side of the story, I would be sceptical.
I wouldn't hold it against someone if they bitterly regretted leaving a relationship in such a cowardly way and had uncovered their own character weaknesses which had in the past, led them to have an affair rather than sort out the problems in their marriage (if any really existed, that is )
It's what he's not saying that is hugely telling. He's saying he regretted his infidelity, but not what he learned from it, or what it was about him that led him to that choice. How he would deal with a relationship differently next time around.
But that's a moot point in your case anyway. I just don't think you should be having a serious relationship with anyone right now and certainly not an existing friend.