any company that values its IP/client lists/etc will (should) run an "activity log" over any employee who hands in their notice, typically for the 3-6 months preceeding the date of handing in notice.

Some poor sap then gets to scroll through it and see if anything looks odd. If it does, they ask someone with more context to have a look.

There is no excuse for expecting this kind of thing would go unnoticed, beyond simply assuming your employer is an idiot.