Possible, yes. A good idea as your plan for emergency communication while hiking on a remote and hazardous trail? I wouldn't count on it.
As you've already observed, although there are repeaters along the way, you have to know what they are, you have to be in range of them, and someone has to be listening.
Consider the things that could go wrong:
- You discover the repeater that you thought would cover this area of the trail is no longer operational.
- You are in a canyon with no repeater coverage.
- You have incorrect CTCSS or other access information which means you can't access the repeater, even if you can hear it and it's operational.
- You are lost, and not be able to figure out what repeater to use, even with a prepared list.
- You are lost, and can access a repeater, but you're unable to describe your position in sufficient detail for rescue crews to find you in time.
- You lack the presence of mind to find your location, consult your repeater list, program the radio, access the repeater, and articulate your situation.
- You can access a repeater, but either no one is listening at the time, or anyone listening is unable to effectively relay your message to someone that can help you.
- You are off your planned course, either because you are lost or were forced to detour, and you don't have access to a list of repeaters in the area.
A much better solution for this use case is a satellite tracker, for example SPOT or an EPIRB. It works pretty much anywhere with a view of the sky, it notifies search and rescue at the press of a button, and it tells them where you are.
Seriously, don't underestimate the probability that you will be lost. It's called "search and rescue" and not just "rescue" because people get lost, a lot. Sometimes they just lose the trail. Sometimes they fall, and they survive but can't get back to their route so they detour, and then they get lost. Sometimes, due to hypothermia/dehydration/hypoxia/hypoglycemia/drug use/etc they manage to get lost when it seems like no reasonable person could. It's not uncommon to find people dead one mile from a trail or road that would have led them to help.
By all means, bring a radio and plan to use it: it will be a useful means of non-emergency communication or a backup in case the satellite tracker is damaged or lost. Bring a cell phone too: you can send a text from a lot of mountain peaks. But I wouldn't count on it as your only means of communication.