BE 2010 (specifically 2010 R3 SP4) remote agent supports Win XP and BE 15 will work with this agent, however this is recommended only during a "rolling upgrade" and thus temporarily only.
The Agent version is of 13.0.4164.0.
So I can add the agent in MMS BE15, and uncheck the option
Upgrade the Backup Exec Agent for Windows to the current version automatically
Restart the remote computer automatically after installing the Backup Exec Agent for Windows when a restart is required
As mentioned earlier, the use of an earlier version remote agent is only for a rolling upgrade purpose an not for continuous backups/restores.
If you do wish to back it up, then yes you add the remote machine to the Backup & Restore tab of the BE media server without upgrading the agent. Restart is not required.