This is not possible if you are logging on the appliance itself.
If however you are logging off box, using the remote agent functionality then it is possible.
You will need to write a script that
1) stops the agent process
2) create a temporary back up directory and moves all log files from current directory that new one
3) restart the agent process
4) process the log files in the new directory once processed remove
The move operation can be extremly quick if you rename the logging root directory and create a new one that is the same name as the original.
However there may be an opportunity for packets to be lost if the service isn't restarted quickly unless you run multiple agents for faulttolerance