Restarting the machine would certainly make the change in circular logging status be picked up in any case, and that means that if you have to reboot to install the agents for your backup product that might be a good time to do this.
As for whether you need to restart anything, it depends if you are in a CCR cluster or not (or a DAG in 2010). If you are, you are in CRCL - Continuous Replication Circular Logging - and that is managed by the replication service. I believe that this will pick up the change without dismounting and remounting the database.
If you are not in CRCL - if you are in traditional circular logging (no CCR, no DAG) - then you definatly need to dismount and remount the database for the circular logging changes to take affect.