yes they get together, after hearing about her curse he doesn't feel disgusted, he feels bad for her that she has to deal with it, that's why she falls in love with him too
I mean this elf here is literally an old hag she's at least the same age as Rudeus parents or even older than that, SHE'S AN ELF FOR GOD SAKE. While maybe they have good romance isn't it will end bitter? While the elf is still young and alive this boy here will get old and died...I mean I'm not against interracial love but love between a different race/species that have different lifetime it will end bitter for one side ain't it? It's better for the guy to not start his love because his love will hurt and destroy his crush in the future when he died earlier and left his lover to live for another hundred of years...