It's amazing how it pops up that one or other is essential at times; so, personally, I'd apply for (and fork out for) copies.
I'm thinking of how (when Mr. J2 and I decided to marry) we had a race against time to receive a copy of his late wife's Death Certificate. He had thought he knew where it was, but 15 yrs. later - it wasn't there and boy, was it a close-run thing (especially as we returned to UK to wed and had to be in residence for 1 month).
Re. passport - mine is still in my maiden name, so a marriage cert. is required occasionally as I don't see any reason to change it before I have to. Hope this helps.