I seriously doubt that. I'm sure there's plenty of little disagreements and whatever on the details as they go along, but I think when it comes to the big picture they're probably all on the same page these days. There's no evidence of a division, even in a superficial 'attitude' way (compared to, say, the 90s and the perceived Conservative Larry vs Creative Bono thing.) Who wouldn't be happy with anything now? They're all pretty interchangeable, it seems.
Mind you, IF it turns out to be Spider-man that kills the May album, Larry and Adam may of course be none too pleased with that, and 99.9% of the fanbase will very quickly do arms deals with that side of the civil war. But I doubt that will be the case, or end up being the reason if the album has been canned. Spider-man really hit the shits after the album should have been done.
Definitely could, but almost certainly wouldn't.