Curious about opinions on if this is a good idea?
In my opinion, a bad idea. You do not have hens. You have pullets so immature they are more "chicks" than pullets. Hormones have not hit them yet, just a group of innocents.
That is not a rooster, it is an immature cockerel. His hormones should have hit like a ton of bricks. There is just no way to predict how he would react to a bunch of chicks. He could leave them alone, he could try to dominate them, which would mean trying to mate with them by force. Not pleasant to imagine.
Integration is never a sure thing, it depends on the personality of the chickens involved, male and female. How much room you have and you integration techniques make a lot of difference in how it goes too. Typically one of the easiest integrations is introducing a mature rooster to a flock of mature hens. He will usually overwhelm them with his magnificence, self-confidence, and personality, then mate with a couple to claim the flock as his, and life is good. No real violence. Sometimes the dominant hen will object or he may not have enough self-confidence to pull it off so it can get rough, but most of the time it works out well.
Introducing a single chicken to a flock has it's challenges. Chickens are social animals and want to be with other chickens. But especially with a difference in ages, once they are together the more mature may treat the immature pretty roughly. There is a potential for conflict any time you introduce a single chicken. Since all these are immature I don't know how all this would play out.
One of the more challenging integrations involves immature cockerels. They have not matured to the point they have self-confidence so they cannot depend on their personality to win admirers. They tend to rely on brute force. A single chicken, a lack of maturity in the boy and the girls, I just would not try it.
When do the girls start acting like mature hens? With mine that is typically around the time they start to lay. With your 15, I'd wait until at least a half a dozen were laying before I'd consider adding a single mature rooster. In Iowa that's probably another four months.
When do cockerels start acting like a mature rooster? I wish I knew. Over the years I've had one (only one) start that around five months. I think a big part of that was that the hens were ready to accept him too. People tend to forget that the girls have a say in flock dynamics too. The latest I've had was 11 months and he had a vicious two-day fight with the dominant hen before he won her over. That was with him raised with the flock. With most of my flocks the transition of immature cockerel to mature flock master is around seven months but most doesn't mean all.
If you really want a rooster my strong suggestion is to wait until next spring and bring in one that is a year old. That should be about as easy as it gets.
Good luck!