During the CICS region recycle, will the incoming request gets time-out? Will the request be logged in some files to check?
It depends... If it is an application in a single standalone CICS region, then yes, requests will timeout unless the architecture (outside of CICS) allows for buffering incoming requests until the CICS region is back and available.
If the CICS environment is setup in an MRO or CICSPLex environment the application can be enabled to handle individual CICS region recycles and even IPL's without interruption.