I have a 17-year-old girl who was diagnosed CRF three years ago when she was 14. She was diagnosed hyperthyroid a few months ago, in August.
I am very, VERY used to dealing with the CRF, but the hyperT was a wrench in the works. In fact, just as you said, once my cat Wintressia had been on methimazole for the hyperT (2.5 mg/day, it's a pink pill) for about 9 weeks, her next urinalysis showed worsening kidney values. She went from Stage 2 (where she had been, very stable, for the three years) right into Stage 3.
She has had some side effects to the methimazole and I'm interested in pursuing the radioactive iodine treatment, which will completely cure the hyperT. As you know as a nurse, medication isn't a cure - she and Midnight would have to be on the thyroid meds for the rest of their lives, on increasing doses.
My cat has never had an abscess or tooth extraction, but she did just undergo a dental cleaning combined with the removal of two small lumps (one on the neck, one on the lower lip, both benign). She came through the surgery with flying colors, no issues at all with anesthesia or recovery.
I think for Midnight, if he developed another abscess, you would have to personally consider the risks, and the things that would happen without extraction. It would probably become painful for him to eat, and he may lose appetite. And the #1 rule for CRF cats is... they MUST eat. So, I'm not a vet, and I can't really give you anything but my opinion what I would do if it were my cat Wintressia with an abscess. I'd do the surgery, because I'd know she'd be in pain if I didn't. For me, personally, the risk would be worth it.
Stryker linked to the best places out there for info/help on CRF and hyperT. :}
Once Midnight's hyperT is under control, your vet will probably try to get you to put him on a prescription diet. I went into this just a few minutes ago on another thread, along with my opinions and experiences with MY cat and the whole "prescription diet" thing. I know you're not at that phase yet with Midnight, but if you're interested:
Right now just keep an eye on him and make sure he doesn't have any bad side effects from the hyperT medication, as it can be kind of rough on some cats.
But basically, TL;DR is my cat is CRF and hyperT and made it through a surgery just fine a few weeks ago, but your cat's experiences and reactions may be different.