No, it wouldn’t. However, most choke holds, and garrotes, for that matter, are designed to be used from behind. So, a head on attack trying to choke someone out is just not going to work.
You can just go for the throat with both hands, but anyone who managed to stay awake through a self defense seminar should know how to break out of that. To say nothing of someone with actual combat experience.
Your character could crush his windpipe with her elbow, which would have mostly the same effect, but without her having to stick around and make sure that, “no, really he’s done trying to breathe and you can let go now.” The downside is, she’d need to be standing right next to him to do it.
Making sure someone stays down is actually an issue with most choke holds. While you can accidentally kill them with a blood choke (where you’re restricting the flow of blood into the brain, rather than the flow of air), most choke holds take a long time to kill someone.
They are useful for subduing someone long enough to get handcuffs on them, or for them to calm down (if it’s an anger thing), but actually incapacitating or killing? That’s a lot of time to spend on one combatant.
I’m not sure how long it takes to kill someone with a garrote. I’ve just never gotten reliable information on that one, sorry.