I’d love to be proven wrong, but I don’t think this happens. If it does, I don’t think it’s successful.
As another response pointed out, we start to break down socially after 6 months in Antarctica. And Antarctica is a pretty good deal compared to Mars. You still have contact with a larger culture, you don’t have to worry about food, and if something breaks, parts show up to fix it.
Here’s what I’d like to see before a Mars mission is considered. Build a self-contained container at the bottom of the ocean, in shallow water, hopefully in a warm sea, in an area not affected by storms. Put your hundred people there, and see how they do over a ten-year period. No coming up for air, no coming up for food, no desperate phone calls saying, “We’ve sprung a leak! Help! Need gaskets!” Nope, you’re on your own. A mission like that would be duck soup compared to Mars. Or better yet, show that you can live on the moon for ten years, with no contact with Earth. Good luck.
We have lost all perspective about what we have on Earth. If we were by some miracle able to travel to a distant star and find a planet like this one, with an oxygen-based atmosphere that needed no tweaking, abundant water resources, abundant photosynthesis, abundant carbon-based life, it would be considered a miracle beyond all measure. Yet we take Earth for granted. We can’t wait to leave. “OK, I guess the bad guys win. Let’s find a new planet.”