Having them lower on a priority list does make some sort of sense but aside from that, no, I don't think we should just let them die.
The experience might show them that they want to live. If they don't, better be successful at suicide at least. There are ways to do that with slim to none chance to survive, if a truly mentally sane person is really determined to die they can do some research and not give anyone the opportunity to save them.
I'm pro-euthenasia in cases of incurable and painful illness though, especially where their life would have long ended if not for half a dozen machines they are hooked onto.







