They might get along, there is always wishing, but I don't think so. I would not expect this to work for the long term. Maybe one cockerel, but not three. A bachelor set up is a pretty realistic solution, or the soup pot, but not them all living together in harmony with your flock.
I recommend you have a plan B, ready to go, cause when it goes to fighting, it can go south in a hurry. Some times people without a lot of experience, don't recognize the signs that they are not getting along until they fight. Most people that have not witnessed a rooster fight, vastly underestimate the violence.
I would keep a fish net, so as to be able to pull them apart, and at the very least, have a dog kennel to immediately separate them.
3 cockerels will start bothering your HENS, and that can cause problems with your rooster.
Mrs K