Thats one of the risks i've always been concerned with when it comes to bark. I use it myself. One of the main things is to make sure the mouse or rat is not wet, so it doesn't stick to it. Even then its always a risk.

As for a snake with a piece already lodged in its throat, I agree with calmolly1, i'd be on my way to the vet if it were my snake. If you're willing to risk waiting, i'd just keep a very close eye on that.

Even if the snake does get it down somehow, theres a chance he will become impacted once it reaches the other end.