Not if those are the only two known destinations known to support life! Then the choice is binary really - go to destination or go back.
> And the first generation of people born in the starship won't exactly be yearning for an Earth they've never known.
I think they would. I've seen this in second generation immigrants. One would expect they'd completely embrace the new country, culture, environment, but I often see them idealizing or yearning for some mythical version of their old country, even if the parents have already adapted and moved on in the current culture. There are two mechanisms at work there, I think, one is rebellion against the old generation, and also if things are not going perfectly well, yearning for an alternative ("the grass is always greener on the other planet" principle).