Agree that you do not need to tell ah about emotional affair right now. you both have work to do on yourselves. But,...
Having been cheated on and I had NO idea for 6 months. I would want to know. If you decide to stay with him, and he works his business out...then he deserves to know so that he can choose to stay with you or not. If you don't tell him (at some point), then you take away that decision from him. I was only made aware of exAs cheating after he decided to marry her and they were engaged. A huge part of my pain from that was having no decision making power. I had no control over my own life with him, since i didn't know anything was amiss. Had i known immediately that he cheated or was interested in her, I would have left him ASAP. I would have had some control and been able to keep my dignity a little more than I was able.
If you stay with him, which sounds like what you want, then he deserves to know. It is a respect thing. I would be prepared for him to leave you if/when you do tell him. BUT, there is also a big chance he won't. His call.