I do know they can wake up out of a tranq dart annoyingly early if you get distracted...
Tranq darts are actually quite effective if the guards remain undisturbed. The trouble with tranq darts is that patrolling guards will wake up sleeping (ZZZ marker) guards if they're noticed, so you have to be sure to hide sleeping guards somewhere out of patrol route. This doesn't raise alert level because the sleeping guy's comrade assumes that he was just lazy.
Unconscious (STN marker) cannot be woken by a simple tap and will cause other guards to become suspicious if the knocked-out one is noticed. So it is a tradeoff -- you can either use tranq darts and be safe from raising the alert level of the base, even if the sleeping guy is noticed, or you can knock them out and be sure that the guard won't wake up, but if he's noticed the base will go up in alert level.
So how long does an enemy stay out after you've hugged them to sleep?
Unfortunately I can't give you a precise estimate. From my experience, I can tell you that it is roughly as long, maybe a little longer, than an undisturbed tranq dart. I think that it is around 6-8 in-game hours. CQC throws are very short term, lasting maybe 10 real-time seconds. Headfirst throws into walls last longer, but not that much. If you have to do a chain-throw to a group of guards, it is best to either shoot them with a tranq dart afterwards, or wake them up again and choke them out, to ensure they don't wake up shortly.
I don't think I have the time to sneak out and wait for a Fulton resupply.
- you don't need to sneak out. Just call in a resupply right on top of yourself. No one will notice.