That depends entirely on what they value. If they value their own safety, comfort, and health, then it wouldn't be rational for them. But if they value the advancement of future humans, honor, fame, legacy, scientific discovery, adventure, and so on (which may seem to be irrational things to value for someone in the first group) then it would be rational.
There are some people who will be excited about the fictitious ad from Earnest Shackelton "Men wanted for hazardous journey, small wages, and bitter cold, long months of complete darkness, constant danger, safe return doubtful, honor and recognition in case of success."
Who said they're never coming back to Earth?
>no perfectly rational, mentally healthy human would volunteer for such a mission
That's an easy problem to solve, as there are no "perfectly rational" and/or absolutely "mentally healthy humans", and have never been anyway.
And people can still be quite rational and mentally healthy and yet cherish the possibility to take such a mission, even if there's a possibility to die, etc.
In fact, it's needs no more troubled people than those that go to the army and are OK to be sent to war, or people that dive and explore the oceans, etc etc.
The thought of dying isn't the inherently problematic part, but rather the extreme isolation. People who go to war are there for only some months and have plans for going home, back to friends and family. People who dive and explore the oceans are isolated for a few days at worst; perhaps months in a nuclear sub, but there you have already a pretty large crew around you. Compared to decades spent isolated with a handful of people, and no return ticket to the rest of humanity, those are nothing.
Huh?
"The first crewed Mars mission would be expected to have approximately 12 people, with the primary goal to "build out and troubleshoot the propellant plant and Mars Base Alpha power system" as well as a" rudimentary base." In the event of an emergency, the spaceship would be able to return to Earth without having to wait a full 26 months for the next synodic period."
https://en.wikipedia.org/wiki/Interplanetary_Transport_Syste...
NASA, I believe, is currently trying to solve the problem with more efficient engines for interplanetary travel. Ion drives seem to be the preferred method, but there is still some research going on in nuclear thermal rockets.
Floating around in aerostats on the cloud tops of Venus where it's roughly room temperature at 1 atm on the other hand... or living on the Moon where you can at least communicate with Earth in roughly real-time and are only 3 days away...
Human psychology is another, perhaps even bigger problem, also independent of destination. We've had various experiments with prolonged isolation, but none where the subjects know that they're never coming back to Earth. I'd say psychology has a >50% chance of wrecking the first manned missions to other planets/moons, unless we send huge ships with hundreds of people.
In the Red Mars trilogy by Kim Stanley Robinson, the author has come to the very astute observation that
a) no perfectly rational, mentally healthy human would volunteer for such a mission
b) there will necessarily be extensive psychological screening to ensure we only send rational people
thus c) the people who will be selected are likely to be non-rational actors very good at concealing their non-rationality from psychologists. Also known as people with psychopathic tendencies.