As long as you have the redirects in place, I wouldn't expect there to be much effect for the other branches. Depending on how you redirect the pages and how many inbound links they have, you may actually be able to give some other branches a little boost.
The only ways I can think of that there would be a negative effect for the other branches would be if...
- There's some crossover of traffic between branches. So, not getting traffic to the one branch's pages (the one moving) would mean that none of that traffic moves on to other branches.
- If the branch that is moving is particularly good at getting inbound links, then you would lose that ongoing increase of links.
I'd be more concerned for the branch that is moving off site and for the user experience.
Let's call the branch that is moving "Branch A." For the user experience, if you redirect all the pages that are currently hosting Branch A pages to other pages on your parent company site. All those people who are trying to get services from Branch A that would have landed on one of those pages end up on an irrelevant page. That's not good for Branch A (or probably the parent company).
For the Branch itself, assuming they currently are getting traffic to the site and have built some level of authority in the niche/region, they will lose all that if they go setup a new site. They will be starting from scratch. They'll have a new site with no rankings, no inbound links, and no traffic. Maybe in the long-run they can improve on things, but in the short-term. It's going to stink.
For both of these issues, the solution would be to redirect all the Branch A pages on the parent site to the new Branch A site. That way the user experience is good (users land on the pages they expected to) and Branch A has a site that, from the start, already has authority and traffic. The down side to this, is that the loss of authority to the parent site by redirecting all these pages, could hurt the other branches. It's hard to say how much without knowing how many branches there are, how many links are going to the various pages, etc.
Just some things to think about.
Kurt Steinbrueck
OurChurch.Com