If you've gotten position on the other guy to the point that you can actually put his own garrote around his neck and strangle him, you really don't need to put the garrote around his neck and strangle him. If you were able to fight your way out of a garroting & take that position in the first place, you're certainly good enough to hold that position and keep him down until the elevator door opens, which it is sure to do momentarily. Once it does, you're free to withdraw. Personally, if I somehow managed to pull off that kind of stunt, I'd probably just opt for the rear naked choke rather than trying to use the guy's own garrote against him. Far, far easier to accomplish than taking his garrote away and using it yourself.
I seriously want to know what kind of Bruce Lee / Jason Bourne people we have around here who can fight their way out of a garroting, take the garrote away, take the bad guy's back, and strangle him to death with his own garrote.
it's possible, but unlikely