Eventually. There’d be a pretty good mess in the meantime, and (especially in combination with other current stresses) some of the overgrazed vegetative species, and some other species dependent on them, might not survive.
The native bison, by the way, aren’t nonexistent. They’re only rare, and gradually becoming less so.
Some are. As you said earlier, most modern dairy cows aren’t: they produce way too much milk for their calves to keep up with, and most would die nastily of mastitis.
Many individuals, even of breeds that may adapt, won’t make it, as they don’t know how to survive on their own. Those that have been managing mostly on the open range would have a better chance; but even those often need human-provided food and shelter to get most of them through the worst of the winter.
Overall: I agree that cattle as such wouldn’t become entirely extinct if all humans either disappeared or cut them all loose; but the adjustment wouldn’t be at all pretty, many would die, and damage to other species would be considerable.