I would think it depends on the hierarchy of the bin and the type of male the alpha male is. I think there is a range of different personalities that come into play.
I don't think I have ever had male on male fighting that have grown up in a bin together, same as females growing up together. There definitely would be a scuffle if I put a strange adult male in with a male and his harem, but just like some of the girls will bully a new adult girl.