Seniorboy had a big GA dental at 16. Previous vets had commented on his teeth needing treatment but had demurred about doing the necessary work. His then new (and now current) vet commented that his mouth was now 'horrible' - and I saw the vet nurse reel back from his mouth when she opened it.
I discussed the risks with her (he had (and has) a little heart murmur and was, after all, 16) but the vet felt reasonably confident that she and her team could take him through. Despite the risks of a GA - which do exist - her crunch thought was that the teeth simply weren't going to improve with age and that bad teeth are potentially very dangerous to any cat, but particularly an old boy, so that we might as well go for it while she still felt reasonably fine about a GA. (I don't think she would do one, nor would I probably allow one, now that he's 19.)
It was a fairly lengthy procedure due to his horrible mouth with, if I recall, an extra team member there to monitor his vitals real carefully - he certainly went through a lot of fluids. (I was given a detailed post-op breakdown) and he wasn't allowed out of the practice until about 17.30 at night when they were happy he was fine. He hasn't looked back though. They removed most of his remaining teeth so I think he now has 5 left and while he occasionally has a touch of gingevitis still, that's now controlled by ABs. He's been pretty fine ever since.
I'm afraid that I don't know about the risks associated with hyperthyroidism but that aside, I think I would go for it if I were you - if the vet is happy to proceed with a GA. Bad teeth can have very serious effects on cats: not only the effect of poisons from rotting teeth/possible abscesses on the whole system but just the pain and discomfort of bad teeth (think how you would feel yourself) and the possible effects on future eating.
Yes, there's always a risk from GA so it's one to discuss with your vet thoroughly. (And with your bank manager re the second mortgage!)