From what you described, it sounds that you are hesistant to get mixed up in a relationship where things are not settled right now. Congratulation on being so aware of that unhealthy dynamic. I wouldn't proceed any further with this relationship developing between you and him as long as he hasn't been clear about you two towards his girlfriend in a way you yourself can predict where they are standing right now (meaning: you meeting her and getting her side of everything). Everything else is theirs to sort out. Personally, I would have a problem with someone staying with his partner for the reasons you stated. But that is your decision to make.
So my only advice here would be to get the opinion and point of view of all involved and let him and her handle their stuff afterwards on their own. Their relationship is theirs to sort out. I wouldn't just stumble into this depending on his word that everything is OK and waiting endlessly for some opportunity to talk to his girlfriend. The risk would be too high for my taste.
Facts: 30, female, bi, v-type relationship with Sward (husband, straight, mono) and Lin (boyfriend, straight, mono), poly-fi and co-primary.