I think it could work either way. If you choose to add them in, you could use diamond-shaped gems as the medium; it would match the overall feel of the game, and probably wouldn't need much explanation. You could put a quick tutorial tip in the beginning to explain them. It could say something like "Collect these to replenish Sanity."
I think I agree with you that it would detract from the overall game due to its nature. It would be less about escaping and more about collecting and searching. I like the idea of being able to unlock an event to do a speed run to collect all of the gems before the time runs out, else, well you lose. The question would be: what would the reward be by completing the event?
Just a thought: how close to the Alpha game are you trying to get?