Yes, people abandon them all the time, rooster dumping is a serious problem. In my area there’s always at least 20 at the local garbage dump (all different breeds, mixes of breeds, and ages) and there’s always new ones each time I go there. The “old” ones disappear pretty quickly, the roosters dumped there don’t live too long.
I doubt any roosters with food, water, and shelter would run away from that to go live in the woods. I could understand them joining a free ranging flock from another free ranging flock, but these ones were most likely dumped.