Yes, that is possible. The automatically session logout will not overwrite the current session log if any session is running or active in timestamp mode.
Click on Session Properties –> Config Object –> Log Options.
The properties should be chosen as follows :
* Save session log by –> SessionRuns
* Save session log for these runs –> Set the number of log files you wish to keep (default is 0)
* When you want to save all log files generated by each run, you should choose the option Save session log for these runs – > Session TimeStamp.
The properties listed above can be found in the session/workflow properties.