VSE 8.5i to VSE 8.7i isn't a patch update, it's a full product deployment. Consequently it's going to be controlled by a suitably configured deployment task for VSE 8.7i that you would have to create or modify.
Just checking in the VSE 8.7i package alone should not result in automatic deployment, even if it's checked into the current branch.
However for testing it does make sense to check it into the evaluation branch first, it just makes it simpler to identify. You should not need to turn off any services to achieve your testing.
Check it into evaluation, and set up a deployment task appropriately for your test environment.
Thank you for your reply! I thought that when I checked in 8.7i that it would be automatically deployed, which didn't make much sense. Thank you for the clarification!