No, it shouldn't matter. Any newcomer will jostle the pecking order, of course, but they should eventually settle in. I think it could be more difficult if you removed the rooster, but kept the same flock of hens together. There'd probably be more fighting amongst the hens for the top spot. Some hens would mourn him too.
If I remember correctly, you turn the hens out during the day, but their range is limited by fencing. I have a friend who takes in older hens, and she said that the ones who used to have a rooster in the flock can be a bit careless because they're used to the rooster warning them of danger. You won't have to worry about that since they can't wander too far.