At times he can, and at other times Supes wins, that is why I said basic version of Supes as opposed to All-Star, Pre Crisis, 1 million and a few others.
In the past he has done so, he has two shotted Supes in a JLA story, albeit he caught him off guard, and one shotted him in a JLA / JSA team up and in at least one pre crisis story, Clark's vulnerability to magic will gather him a few wins here even if not for a majority.
There was a time, maybe 30 or 40 years ago when Superman vs Captain Marvel would have been a 50/50 split fight (or at worst 55/45 in favor of Superman). Nowadays, Superman would slaughter Captain Marvel or any member of the Marvel family in anything resembling a serious fight.
Billy isn't a high herald. He's a solid MID Herald on his best day. Can a mid herald take a win against a high herald? Sure but the HH would have to be fighting sloppy or be distracted/weakened.
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..even the outer hells are indifferent matters for they bow only to potent and archaic Nodens.