The amount of time spent in the hospital after being wounded depends on the amount of damage you take. This means that healing heavily wounded soldiers with a medkit before they leave the mission will not reduce the amount of sickleave your squaddies get -- what matters is how much they take in, not how much they leave with.
How much damage they can take in without being wounded depends entirely on what armor they're wearing. Armor provides bonus health - if they take more damage than the health bonus provided by the armor, they become wounded.
This means that adding Nano-weave Vests to your soldiers reduces the chance they need hospitalizations, even after being shot, as it gives an additional 2 hitpoints worth of "fleshwounds" they can suffer.
How much "Bonus HP" your units have is shown on the loadout screen - for example, they'll be displayed as HP 10 + 3 (combat armor + nanoweave vest).
In general, there is also an Officer Training School bonus that reduces hospital time.
That said, the simplest answer to your question? Don't get shot. The more damage you take, the longer the time off. Avoid damage as much as possible to minimize hospitalizations.
These are what grant you XP and how much:
- Alien Kill 30/60*
- Regular Missions 60/90*
- Storyline Missions 120/180*
- Zero KIAs 20
- Resist Psi Attack 10**
- Successful Mindfray 20**
- Successful Mind Inspiration 30**
- Assist Mind Inspiration 30**
- Successful Psi Panic 30**
*Additional XPs earned if the soldier has a rank of Lieutenant or less and kills any of the higher alien ranks (Ethereals, Sectopods, Elite Mutons, Sectoid Commanders, etc.) during the mission.
**Psionic actions.
Your soldiers have different requirements for promotions:
- Rookie 0
- Squaddie 90
- Corporal 300
- Sergeant 510
- Lieutenant 745
- Captain 1100
- Major 1560
- Colonel 2150
- Psionic* 0
- Specialist 50
- Operative 120
Source: http://ufopaedia.org/index.php?title=Soldiers_(EU2012)#Earning_XPs
Best Answer
The aliens never wake up from their tasered state.
Keep in mind that they are still vulnerable to damage and an alien grenade, car explosion or rocket blast in their proximity will still kill the neutralized aliens, depriving you of a live captured alien.