The mechanism is slightly different, as is the physiological response, but I believe it’s relevant.
There is a group of people who specialize in causing loss of consciousness via restriction of the carotid arteries - grappling martial artists who fight for submissions. Practitioners of judo, submission wrestling, modern mixed martial arts and particularly, Brazilian jiujitsu do this on a regular basis. Of course, the idea is to tap out when the other guy locks in, but on a fairly regular basis, people do pass out.
First, a clarification of terminology. By mistranslation, convention and convenience, most martial artists switch the terms “choke” and “strangle” from the standard definition to mean blocking the arteries and blocking the airways, respectively, though often, the terms are used interchangeably. For this post, when I refer to a “choke” I am referring to blocking constricting flow, not air flow.
Most simple chokes work by constricting both carotid arteries at once. You can google “rear naked choke” or “triangle choke” if you’d like to see the positioning. Pressure on the throat/direct pressure on the trachea to restrict breathing is possible, but is generally regarded as inefficient. The general idea is to get two limbs, either his or yours, on either side of the neck. Then you apply leverage and squeeze.
Once a good choke is locked in, loss of consciousness happens anywhere between 3-5 seconds, depending on the individual. Any choke that takes longer is because one side of the neck or the other simply hasn’t had enough pressure applied to it.
This is why you will see fighters tapping out within a second or two of a proper choke being locked in. The effects are almost instantaneous. A fighter who waits a second or two too long usually ends up going to sleep. Lasting more than 5 seconds against a set rear naked choke is simply just unheard of.
I can’t speak to the spinal cord severing nor to it’s neurological effects, but from an available oxygen point of view, you only get a few seconds at most.
The X factor in this is that it’s very difficult to only restrict the carotids without constricting the jugulars or hitting the pressure receptors that run along them. You know the moment when someone’s slapped a solid choke on when you start feeling an incredible pressure in your head. (This is generally a pretty good indicator that you should tap immediately.) So there’s the chance that loss of consciousness during a choke is due to a drastic change in blood pressure and not necessarily the carotid artery restriction.
There is some conflict in the literature about the causal mechanism of LOC but one way or another, the head gets five seconds at most when the blood vessels are completely or almost completely restricted.
Again, while I realize the mechanism is different, it’s about as close as you can get. Without fresh oxygen or when something drastic happens both sets of blood vessels, 3-5 seconds.