A quick clarification needed for statement in bold above. That behavior is much more likely to be exhibited by hatchery-sourced backyard roosters than it is by game roosters.Agree with all others. I would be upset if a flock of chickens started frequenting my property, mostly because of my own chickens. I wouldn't want to risk the roamers bringing something to my flock, especially since I sometimes allow my flock to free range on my property. We specifically herd them back when they stray from our property, and they've honestly come to learn not to roam too far.
That said... If your neighbor's dog was roaming, but you knew it was your neighbor's dog (even if you didn't know which neighbor) you couldn't just grab him and give him to somebody else. Especially now that he appears to be going home somewhere each night. If this was happening, you'd call animal control or the cops. You could file a nuisance complaint, which they'd have to act on to the owner. Especially if/when those cockerels mature more and start fighting, they may see you as competition to the ladies and could go for you or your husband. That's not something anybody needs to deal with, especially if the problem isn't their responsibility.