The Abrams has an NBC filtration system, rad detection kit, etc. Allegedly, you can overpressure the crew area to keep out the fallout. Uh, not sure how great those seals are. No one is really wanting to test them in the real world. The NBC specific vehicles are the only ones that folks maintain properly. You'd want to be wearing your MOPP suit and mask regardless.
Rads do not effect the munitions of an Abrams.
If the seals work out, you should be able to withstand the overpressure in an Abrams. That's the most dangerous part. If the overpressure system works, the fallout (second most dangerous part) is minimal. You'd want to keep your MOPP suit on and shag down to the nearest decon station to get the fallout washed off the tank. Then get individually decon'd.
Sustained fighting in an NBC environment is probably suicidal, because something will eventually fail. If it doesn't fail immediately.
The US Strategic nukes are the W76, W62, W78, W87, and W88. We don't have "TacNukes" anymore. Sorta. We have Dial-A-Yield. You can set the yield on the fly, and make the nuke either a Tactical or a Strategic nuke. Those are the W80, B61, and B83.
Disclaimer: I have no idea if the above is accurate. We may or may not have "off the book" designs such as Atomic Demolition Munitions or whatnot. Not my area of expertise, and it'd likely be classified anyways.
My coworker was under the impression that any tank within 2 miles of a 20 kt blast would be rendered useless, whereas I suspect perhaps only the tanks within a couple hundred yards would be mechanically "destroyed" whereas the tank crews would be the weak link for tanks outside that range (possible injured or killed by overpressure). If the crew were later replaced, I believe most tanks would be more or less operable with only superficial damage.
No, a tank within "a couple hundred yards" of a 20 kt blast (assuming it wasn't a couple hundred yards of lead and concrete) would fry. One, the rads would be fatal. Two, the seals couldn't possible handle the overpressure. Three, wouldn't matter because the entire tank would be cooked. Certainly enough to kill the crew, detonate the rounds, set the fuel ablaze, melt anything not metal, etc
The hull would probably survive. As a vaguely tank looking lump of radioactive metal.
2 miles from a 20 Kt ? Probably survive just fine. Just wash it off and decon.