I know folks have horror stories on keeping roosters, but I never have, I do also get rid of the duds if I have too. No room in this house for a mean rooster. I have kept roosters with all my flocks, and feel that the positives of keeping a rooster out ways the issues of keeping one.
I will admit that your hens will be stressed at first especially if he is a bigger boy and grows confident enough to assert himself. He may jump on them and "force himself" on them, this can be very upseting for people who aren't use to it as the hens do scream if they have never had it happen before. He may rip out a good number of feathers getting them to listen to him. This will cause a chain reaction that may be hard for you to watch as the hens will start reasserting their hierarchy with each other , the girls at top will be fine but your girls near the bottom may start getting picked on until everyone feels comfortable again. There is also the matter of what if 6 hens are not enough for him, when my roosters are young it isn't uncommon for his favorite hens to go with ratty or bald saddle feathers for some time until his urges calm down.
But I love having a rooster. I have just never had a dominate hen ever do the things a rooster does as well. The first time I saw a rooster dig up a worm only to call his girls over to give it to them, I knew what to look for in a rooster. Don't settle for a subpar rooster, there are many people out there trying to find homes for roosters. If your rooster doesn't give the hens first dibs on food or watch out for them get a different rooster and have yourself some chicken soup. The only reason to keep a rooster otherwise is if you are breeding for looks etc. But I only care about temperament... and egg size. lol
I agree you should not add him immediately, keep him quarantined near your girls, not just because he may carry mites or other issues, but also because they are likely to peck at him as well especially if his rump is red and sore from lost feathers. Depending on their breed and temperament, will make this process either easy or hard. If you have a "sick chicken" coop, move it over to their run so he can live near them and they can start seeing and hearing him. His feathers will regrow, he may need a protein boost depending on the loss, but so long as their are no open wounds you don't need to put anything on the wound.
What breed is the new rooster and what are your hens?