You are dealing with living animals, no one can give you any guarantees as to how they will behave. I've never had a mature dominant rooster harm one any chick, his or some other rooster's, but some people I trust on here say they have. I think how much room they have has a lot to do with that but even with wide open spaces anything is possible.
I have a lot of room and I typically raise my cockerels with the main flock until they are butcher size, typically around 23 weeks for me. What normally happens is that the chicks are fine, male or female, though they stay by themselves away from the main flock after the broody hen weans them. When the cockerels hit puberty and their hormones drive them wild they start trying to mate the pullets they were raised with. The pullets don't want them to so they run away. It can get pretty hectic. My adult rooster pretty much ignores this. But when those cockerels start to bother one of his hens he really objects. That's practically always just running and chasing, no real fights, but I have enough room that the cockerels can run away and get away.
Each chicken has its own personality. It is possible your RIR wouldn't stop until he killed a rival. It's even possible he would harm a chick though the other hens are most likely a bigger danger. My broody hens handle that.
You never know how many eggs will hatch. You never know how many will be male or female. With your history I'd have a plan to manage any cockerels from that hatch by the time they hit puberty. Good luck!