From the amount of destruction you bring to the Brotherhood in the footage (firing a missile at an initiate, bombing a vertibird, taking down their whole ship), as well as you attacking synth soldiers, I think it's almost certain you can join one side or the other (maybe more). You have to remember that the BoS are really not nice guys. Lyon's chapter went native, as it were, but I doubt Arthur would continue along that path. Lyon's, by basically going rouge, kinda had Arthur excommunicated from the order his ancestors created. On top of that, NV shows that the real BoS isn't doing well at all. He may be resentful of what happened to the BoS, a society he was meant to lead, and decides to go full agro.
The Institute is said to be a place of un-heard of technology. It's also hinted that they are having a growing problem of their robots trying to get free. Arthur may see this as a chance to kill two birds with one stone; expand his chapter AND secure some super tech.
I hope this to be the case, because then it paints both factions as morally grey. The BoS is trying to take land and tech by force, while MIT (shorthand for The Institute) is trying to, through doubious means, rebuild (the area shows a bit more built-up city, maybe MIT cares for people but enslaves robots?). Help one and you're aiding in a hostile invasion, help the other and you're condemning synthetic lives to remain slaves.
I also have a mini-theory that Arthur may have contacted the MWBoS. You see airships (something they were known to have, even if the ships were destroyed the knowledge to build them is still there), and IIRC the MWBoS were the only chapter to really operate as a nation (expansion, recruitment, etc). The normal chapters never really seemed to do that. Sure they'd attack places with tech they wanted, but they always seemed to go home after. With the original BoS in near ruins (NCR war and their refusal to adapt), Arthur may be looking to a successful and thriving chapter for guidance (Tactics shows that they're doing great. Especially with Barkely's ending).
/baseless speculation