I have long-term plans for TuP as we get closer to Affiliate level in terms of the necessary pivoting they'll have to do, but honestly the political and cultural issues are big enough that @OneirosTheWriter could conceivably put a Apatia-style block on membership if he wanted to, or they could cause problems down the road like @Simon_Jester said. I'm not in control of any of that though so Who Knows.
I really should write a thing about them though, they've been pretty overlooked
However, I'm not sure it's the Orion war that will bring TuP around. They're based on two major principles that counter the Federation: Orion for Orions and a belief in a return to the glories of the Empire; and that the Federation's economic and bioethical outlook is wildly diverged from what is compatible with Orion society. Obviously the Syndicate is bad, but Federation and Caitian boots on the ground stokes paranoia in their base and in general about becoming an occupied state [for IRL parallels, consider people afraid the UN will invade]. Now that might change, but what I think TuP would be doing is mostly waiting it out and hitting the government with withering criticism for the failures of Starfleet. Ultimately what they hope is that Starfleet will withdraw before the fight is really over, and then they'll sweep Congress from power, claiming that Congress' vaunted Federation isn't actually in it for the average Orion; that Orion blood was spilled over the Federation's temper-tantrum about a crippled ship and they left Orions in the lurch. Which wouldn't even be entirely inaccurate.
In the event of an actual Syndicate defeat obviously yeah, they'd have to change their tune. But in any realistic timeframe Congress may well be out of power by then anyways, in terms of natural election cycles.
