Does "Those Who Hunt Elves" have a definitive ending?
Actually, there where two manga series:


Those Who Hunt Elves that was adapted almost entirely in the two anime seasons, and
Those Who Hunt Elves Returns, years after the ending, with new stories not directly continuing but mostly reusing the same characters for new adventures, but was very short.


Finally (for now) in 2013, the author continued with a new manga, also an "unconnected" continuation, with the same settings and characters but not exactly a sequel since the plots were already closed.

As for the plot that you mention, in the first manga, it was resolved somehow, but keeping the door open for those sequels.