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Yes, it will work and details are provided in the below section.

Definition of Private mode is provided in the link :

https://help.sap.com/viewer/f146e75588924fa4987b6c8f1a7a8c7e/7.5.9/en-US/4932f2b4e92e3504e10000000a421937.html

 

When the work process enters into PRIV mode, the work process is reserved for processing the current user context until the context releases the work process again when the request has ended. Up to this time point no other user context can be mapped to the work process . The parameter definition of rdisp/gui_auto_logout can be found from RZ11 transaction and it means that a user context gets logged off if it is inactive, per definition an user context is active if it occupies a work process i.e, the parameter rdisp/gui_auto_logout does not count if a work process is allocated by a user. Indeed, it does not matter if this is a PRIV mode or any other status.

Scenario 1: 

If the user context has released the work process i.e user has ended the running transaction and user context is idle, rdisp/gui_auto_logout begins.

Scenario 2: 

If a user has executed a report or program and it has finished execution and fetched output ( however user didn't end the running transaction ) i.e user context still holds the work process, then the dispatcher checks if a user context is active and in this case the user context is connected to a work process and so it is considered as active which means the user cannot be logged off.

If you need to control this behaviour of logging off user in case execution is finished but user holds the work process in PRIV , you can set the parameter rdisp/max_priv_time to reset the PRIV mode. After this reset , the time for rdisp/gui_auto_logout begins.

More information about PRIV management is given in the note 2098461 - PRIV process management


Note :

Changing parameter rdisp/max_priv_time is your organisation decision as we never know the time a program needs to finish its execution. If there is not enough Extended memory, the work process goes into PRIV mode (this is not an error) , it may take a long time to process and if the parameter is set too low, this will cancel the processing of the Work process. Such setting may cause more problems than the long process on PRIV mode.