I have found that most remote server reboots are required when you push the AOFO (Advanced Open File Option) agent package (setupaofo.cmd). Although the seupaa.cmd will work, I have found that it does not always install all of the hotfixes on the remote server. If you do a push upgrade, all of the updates are pushed at the same time as the upgrade. Also, you can push more than one server at a time. I have opted not to reboot the server right away on all the servers that required a reboot after the upgrade from 12.0 to 12.5 and had no issues with the backup operations. The servers were rebooted when microsoft patches were installed.
One thing to note. If the server requires a reboot after the upgrade, you will not be able to push a hotfix to the remote server until it is rebooted. The setupaa.cmd does not tell you if a reboot is required, but the remote push will prompt you.
Hope this helps you make the decision which is best for your environment.