Most, but not all, domestic animal species would survive and breed, though in pretty much every case they'd be much reduced in number. In the long run, as evolution had its way and the ecology adapted, it would not be surprising to see some species die out completely.
In the cases of dogs, pigs, cats, and horses, we already have feral populations, and sometimes have had them for centuries.
The milk cow breeds would probably die out, but there are plenty of other breeds of cattle (including some much-less-overbred "heritage" breeds) which may wind up doing OK. Remember that 99.9% of the individuals in a domestic species can die but still leave a viable wild population. Sheep likewise: Huge die-offs, but some rare breeds might well survive. (Of all the large animals, sheep look the diciest.) Goats would probably make it.
Chickens run wild in some places now. Their numbers would doubtless decline, but they'd quickly re-adapt to lay fewer eggs and have a more practical body type.
Domestic turkeys probably wouldn't make it, but there's still a thriving wild turkey population.
The key point here is that there are two stages: The first stage is whether a domestic species can survive in the wild as it exists today and breed successfully. Most domestic animal species in North America would survive the disappearance of human beings and establish breeding, wild populations.
The second stage is how ecological adjustment works out over the longer run. Will the more marginal species adapt to the wild and thrive long-term or be wiped out before they have a chance? This is basically unpredictable, depending so much on chance. (E.g., a hard winter early in the process during a time when a predatory species is overpopulated could wipe out a marginal population that might otherwise have re-adapted to the wild.)
So, domesticated animals would die in very, very large numbers, but nearly all of them have a decent chance of surviving as species somewhere.