I mean... vampire bats breathe (I would imagine), but if we are talking about the undead, re-animated corpses who are not "alive" thus do not need to do the typical things that an alive person would, I guess it could depend on the genre? :-D I think you are correct though - it would help them blend in better if they would do some of the things that normal humans would, especially without having to consciously think about it.
Like in the Castlevania Netflix anime thing, vampires were basically immortal super-humans (whereas Dracula himself was somehow... alien), so vampires weren't so much "undead" as just a different variant of humanity, perhaps a blended variant like base human DNA + virus alterations - and anyway, they more or less seemed "alive" there, hence you would think would benefit from oxygenation of their bloodstream, even if the level of their dependency upon such were reduced. I think Blade's vampires might also have been of this sort, but there is a whole comic book series iirc and I never read any of it so definitely don't quote me on that.
But in series such as Buffy & Angel and John Carpenter's, vampires were more "spiritual" like a curse passed down from ancient times (in the latter, from Judas who betrayed Christ), and their immortal bodies were animated by magic so that sort could go without any oxygen whatsoever for like millennia and be just fine.