Part of the reason prey populations are out of control is the abundance of food available to them. You’d probably be able to support more wolves than historically there ever were with such populations. Hard to say if this will lead to a significant dent or not all that being said, reintroductions don’t always play out as expected. Every time you go up a “level” of the food web e.g. from plant to plant eater to predator, in the best cases the absolute numbers are 1/10; eg 100 plants can support 10 rabbits and 1 predator. If there are now 100 rabbits theres probably 10x as much food as before. Having that many rabbits means whatever is around that eats them e.g. coyotes or bobcats population as also went up 10x in that time. Therefore even if the wolf entirely displaced all bobcats or pumas or coyotes or whoever, the amount of prey being eaten might not change really. Who eats them might change, but maybe not their absolute numbers.

I would imagine that Coyotes are a bit more opportunistic and rely more on scavenging and hunting smaller pray they can tackle on a solo hunt such as rodents and rabbits, but occasionally doing the big game pack hunt. For Wolves I would thing the pattern is opposite.

So while their ecological niche somewhat overlaps, it does so in a complimentary way, that is—and this is me being an armchair ecologist—the presence of Coyotes may only encourage the Wolves even more to go after the large gracing pray in packs as the competition is too tough for scavenging and the easier solo hunting of small pray.