I wouldn't let it keep you up at night. Lots and lots of old cars have sat for much longer than this. I think your worst case scenario is that the carburetor might need a deep cleaning, and maybe just replace the fuel filter while you're at it. Could your tires get flat spots? Maybe, but they're a wear item anyways and it isn't detrimental to the car if the tires need replaced in order for it to come out of hibernation. It would be a bummer if your tires were brand new and you ended up with flat spots, but it wouldn't be the end of the world.
Hopefully you're well enough by spring to get it back out on the road. When the time comes, just make a checklist and inspect everything like the brakes, fluid levels, and the condition of the tires before you start laying rubber again. It wouldn't take very much driving to burn off a half a tank of old gas and then you can start over with a fresh tank, see how it's running, and take things from there.
Sorry to hear about your stroke, hope you get better!
'66 SS Clone
Fast Burn 385hp Crate 350 (for now)
Muncie M20 & 3.42 Posi
UMI Stage 2 Suspension all around