...and the pesky fact that they have nothing to gain from fighting and everything to gain (at least short term) from allying. But other than that!
As a favour to Yuri, Urek stole the baby zygena knowing it would piss off the Yeon family, killing several rankers along the way and he threatened to kill Gustang's whole family if he didn't give Hell Joe's soul back. I'd say it's more naive to think Urek will sit back and do nothing as Yuri is executed.
Which is basically what I just said above, with specific examples. I agree.
Most likely Wingtree as a whole won't take action, but those that want to will. Such as Urek and the ones who went to 2f with Yuri.
This I less likely agree with though. Urek
IS WingTree (and to an almost equal extent Baek). If Urek steeled himself with the resolve to go against Zahard formally (not one of his side-quests) then I don't see the bulk of - up to and including Baek even - joining in. And Yuri is such an important character to WT I can't see the OG's in the organization turning a blind eye. If Yuri herself - a non-member - can activate a WT ranker cell to go accomplish her own personal task of retrieving a 13mo (something not even of use to WT) then I imagine Urek could activate the whole damn lot of them (if he thought they'd be needed) to stop Yuri's execution or even join Baam at some later point.
And as far as Yuri being a non-member... She's as much a non-member as EVK is not a member of FUG - that is to say essentially a member at this point. She can form groups entirely of WT members to go accomplish tasks that aren't in their mandate or even useful to the organization. She was there at the FOUNDING of WT. She can involve herself in the nomination of WT members and refer them to the CEO, Urek (something that not even every other member can do short of those with enough 'wings'). And most importantly she's a very important person to Urek, the defacto boss. (she can even verbally shit on Urek and not expect him to do anything about it) She just can't be an official member because of her Z status (it's not allowed), although she basically is a founding member and non-official figurehead.
Nevertheless, Urek *alone* is more than enough. Even if the others don't join/aren't activated.