I'ts all relative. With respect to capability, just about anything can tow anything, but with tradeoffs on longevity and speed. You have seen trucks in TV ads pulling impossibly huge things. Sure they can do it, but how quickly, and can they stop it once its rolling down hill?
On the practical side as others have said, the Avalanche is probably outside the weight rating of your tow vehicle. That is the tow bar is not rated for that heavy a vehicle. You could have the frame and tow bar beefed up, but this is not a standard operation and it would depend on how much you trust the person that does the upgrade.
With respect to tow brakes; since there are precious few automobiles that weigh under 1000-2000 lbs (limits for brakes in most states) any modern auto used as a toad will need auxilary brakes.
I have to side with dawg, I wouldn't do it.
2002 35R Southwind, W22 8.1L Vortec UltraPower, 19.5' wheels
Toad: Wrangler, lifted and on 35" tires