If I knock out people will they eventually get up or does it not make any difference.
Whilst having no weapon equipped (fists), Edward will incapacitate the target rather than kill them. This does not count as a kill and you will often see the target rolling around in pain on the floor. They will never regain consciousness.
Using "fists" on a kill target will change the animation to show the neck being snapped or something of the like. Trying to emphasize the death of the target.
There is also some "fist" animations which look like you kill normal enemies. These do not count as a kill though, so will not fail "do not kill" objectives.
There is a scenario in which targets will regain consciousness, but that is when afflicted with a sleep dart. Enemies will regain consciousness after a timer expires which is visible above their heads. Enemies shot with berserk darts will die after their battle frenzy wears off.