Batman maybe, superman never. The Covenant only have plasma based weapons which could possible kill batman (he is a good fighter, however), but these guns would have no effect on superman whatsoever. He could crush then, LASER then to death with his eyes, or simply throw them into orbit. Superman could even take on a whole Covenant fleet by himself, simply by ramming himself into the ships and making man-sized holes throughout the fleet.
Oh yeah, what about Kryptonite Spikes and KIB (Kryptonite-Infused Blamite) Needles? And plasma formed from krypton gas?
Superman would lose to this cause it's Kryptonite. Also, Superman could be infected by the Flood if over 10,000 infection forms jump at him.
They could beat batman no problem, as for super man, they could beat him too, after all he got no shields and the Convenant have thounsand of troops. The energy sword and needler would make short work of him and is impossible for superman survive carriers´ weapons.