The PRO version will, yes! Internally, it records any activity that creates, deletes, or changes a file to a dedicated log file. You can view this file separately or merge it with the main activity log file to get an chronological and highly accurate view of what is being used.
Windows as well as third party Windows programs usually have background processes that do periodic updates. This usually happens without your knowledge at various times of the day. LookInMyPC will tell you when this happened, what files were updated, where they were downloaded from, and more.
By default, only the most important directories are monitored, but you can add any additional directories you want.