Back in the old days around here deer were scarce. Up until the mid 80's there were only like 200 -300 deer in the surrounding county's. So when a shot was made the old timers used to run and jump on a deers back and cut the throat. (Like killing hogs.)
Well, old habits die hard and they did that until they were too old to do so.
Nowadays the guns/bows/ML's are much better.

But to just outright answer the question, Yes I would and have. It is much quicker than another arrow shot, but you must make sure you cut the wind pipe and not just the skin. I can't stand to see an injured deer suffer. Cut the throat and within 2 -3 minutes it's over.