Some of the smaller defensive ends and maybe some tight ends could, but weighing 250 lbs, let alone 350 or even 400 lbs is absolutely no joke for any aerobic exertion over a few minutes.
I think this is a case of how us runners tend to fall into an echo chamber and think X time is unimpressive cause all of us and our friends who were highschool/college teammates that are top 1-10% talents that specialize in the event could do it pretty easily.
I think if you were to test a couch 300 lb dude against a collegiate football 300 lb dude the the difference in Vo2Max relative to bodyweight as well as strength to bodyweight would be astounding (no duh) but I think it would be uncommon to see any of these guys running a sub 8:00 mile and very rare to see a sub 7:00, let alone 6:2x miles for 3.1.
I remember in highschool gym class a good friend of mine who went on to be a D1 right tackle ran about a 9:30-something mile and just about passed out at the end. He put on a good 30-40 lbs going into college too. The difference being that the kid with similar size to him ran at 10:00 pace for 150m, and then walked the rest of the mile in god knows how long huffing and puffing and holding the whole class back from moving on.
I played highschool ball until 10th grade and obviously there’s a large leap in athleticism from HS to collegiate football, but what I saw even out of our college prospects tells me the answer is probably no. In my final season with the team I’d whoop the entire squad including skills in conditioning violently except for one other guy (who ended up being a 49 400m guy as a junior and ran a 4:47 mile the one time he tried it) when I was in roughly 19:30-20:30ish 5k shape.