Expect residue or damage.

Yes, the adhesive base can leave a sticky mess or a permanent stain on a wooden desk after two years, especially if the mousepad has a gel or tacky backing (not a simple rubber gripper).

Those cheap sticky pads work by being slightly adhesive, and over time that adhesive bonds to the finish—or seeps into unprotected wood. Heat and humidity make it worse. When you peel it off, you might leave a gooey layer, pull up the finish, or get a cloudy mark.

If you already have one on a nice wood desk, check it periodically by lifting a corner. If the pad is significantly tackier than a rubber mat, I’d remove it now and use a regular rubber-backed mousepad instead. Future You will thank you.