I insure Max with Axa, and didn't start his policy until he was about 7-8, so it is possible to insure cats when they are a bit older.
Max also has FIV so had to log that as an existing condition, and figured they would try and exlude pretty much everything if they could try and relate it, but in the last year I've had payouts for kidney, thyroid and urinary tract infection, so they've been very good.
I think with any policy they would take the hyperthyroid as an existing condition so anything related to that would be excluded, exactly what else they would exclude would depend on what was wrong, and how good your vet is in convincing them that the items are not actually related
I know that thyroid can also affect other organs, but if ongoing treatment for this can be proven, then hopefully this would bode much better than issues which have arisen through non-treatment, if that makes sense?
Defo get a quote, you might be surprised, and the insurance really has been a lifeline for me this year