Not impossible
just highly unlikely
Welp, I just finished off the last quest. Ended up siding with the Institute. The ending was... kinda abrupt. I was expecting a little more honestly. Oh well, at least it's not a hard stop like Fallout 3, you can go straight back into the game world. I think I have all of the side quests cleared though, so there's not much to do besides settlement building and radiant quests. I will be back for DLC for sure though.