The reason I would still recommend a full geo check in this scenario is that the car most likely hasn't had one for a while (if ever).
At 10+ years old, everything would have fallen out, though the big killer for Omegas is the way the front camber falls out of (even GMs piss poor) spec, though other stuff will be out as well.
If the rear is out, everything is out. 4 wheel alignment/laser alignment and just guff does not set the rear, only use it as a reference point for the front... ...so if the rear is out, they will bugger up the front by adjusting it.
After years of suffering chronic tyre wear and pulls on my first Omega (the Silver Bullet), it now gets an annual WIM check, along with every subsequent Omega I've had. Other cars I've had I tend to only get WIM'd once, as they don't appear to fall out of adjustment like the Omega does.
I would also add, the Silver Bullet, despite its 204k, is one of the straightest, sure footed cars I've ever driven (shame I'm struggling to get TBE to the same level, but its getting there), followed 2nd by Tractor, which also had regular WIM visits.
There are DIY ways of getting it close, if its only one setting you've disturbed, and the car's geo was bang on before (only known if you have recently had it checked), but they are very fiddly. I believe they are more for getting it "near enough" so as to be drivable, and not wreck the rubber, until you can get it done properly.
For an Omega, I would always class any form of tracking/4wheel alignment as a waste of money, as its the wrong service for what the car needs.
As to 2nd hand TREs. *sigh*. They are only £20ish from GM. The GM ones are by far the most durable. I think the trash that Autovaux sell as genuine GM (and clearly aren't, the lying 'tards) are probably the worse I've seen, not lasting the warranty period. 2nd hand is just a tad daft IMHO.