Well, sort of.
Marvel has never been averse to crossovers and cross-promotions (the character Dazzler was originally intended to be marketed along with her own album). And in 1984 Letterman made a special appearance in the Marvel universe when The Avengers (well, not the POPULAR Avengers) made an appearance on his show.
Of course everything went wrong.
They were attacked by Fabian Stankowicz, the slightly less popular Avengers ran into some trouble subduing him, and the in-house band opted to continue playing to avoid panic like they were on the sinking Titanic.
Letterman managed to save the day.
So, while he'll probably never end up in a cape and spandex (we hope?), he did manage to upstage the Avengers at their one job: saving the day.