Yes, though this is made much easier through third party software. I've used the program Sharemon (shouldn't be difficult to find) for years, and it reports who is accessing what.
Enable Audit Object Access in Group Policy. Go to Computer Configuration\Windows Settings\Security Settings\Local Policies\Audit Policy\Audit Object Access. Enable Audit Object Access. Right click on the shared drive->properties->security tab->advanced->auditing. Add the users or groups you want to track. Events will be recorded in the System Security log. Access it with Event Viewer.