
Does this sentence really match its English translation?

Yes, it matches.

But doesn't 「添い遂げる」 means rather something "to be/ to remain a faithful husband/wife till death" than just "to be married"?

It can mean either that or ‘to overcome all difficulties and eventually become husband and wife’ (according to the Kōjien).

Please also check here:
http://dictionary.goo.ne.jp/lea...%92%E3%82%8B/.
It’s the second meaning.

Thanks, Lisa!
I think, it would be really nice if Jim Breen has added "to overcome all..." meaning to his JMDict/EDICT, too. :-)

Maybe you should suggest that to him. ☺
I always use the Kōjien to be absolutely sure (love that book). ☺

Kōjien is undoubtedly great, I reckon. :-) But I'm afraid this book is too tough for beginner learners. :-)
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Ma hema nêeşkenîme dîyar bikerîme ke na cumle açarnayîşêk ra virazîyaya yan ney.
hetê endamêko/a nenas/e ra ame girêdayene, tarîx nêzanîyeno
hetê endamêko/a nenas/e ra ame girêdayene, tarîx nêzanîyeno
hetê endamêko/a nenas/e ra ame îlawekerdene, tarîx nêzanîyeno