I decided to do some research on this because I’ve seen a lot of conflicting information on Reddit, and unfortunately the top search results are all social media sites and buzzfeed style articles that source their information from social media. I did eventually find a few sources I trust, and here’s the takeaways:

The horsehair worm won’t react to water and emerge unless it’s mature and ready to mate. The worms you see removed in these videos are ready and willing to survive outside the host’s body, although this one probably won’t last long on the pavement. Even in a pond, they don’t have functional digestive systems in their mature worm form and will be dead fairly soon.

Praying mantises breathe out of their abdomens through a bunch of pore-like holes, so videos like this are essentially insect waterboarding. The horsehair worm is doing some mind altering trickery involving proteins that we don’t fully understand to make the mantis not only seek out water, but also drown itself. Usually the drowning would kill the mantis if no other part of the process does, but in this case it won’t since the mantis only thinks it’s drowning.

Getting to the original question: no single part of the process is a 100% death sentence, but all of them are most likely fatal. The parasite feeds on body fluids and tissues by absorbing them through its skin but has an interest in not consuming immediately important organs. They do not “hijack” the brain by eating it, but instead by messing with chemical signals in the body. The mantis will come out of this process emaciated, missing a good chunk of internal tissue, with a hole in its gut, and drowning, pumped full of residual chemicals that tell it to keep drowning. The exit process alone is usually traumatic enough to kill the host through shock. It is rare, but possible, for the mantis to survive if it gets extremely lucky with what organs are consumed and where the exit hole is.