Yes, especially with cheap rubber.

The adhesive in non-slip mats or rubber bases can absolutely leave a sticky, gummy residue on bare wood if left for months or years. It’s not a guarantee—some high-quality silicone or thermoplastic mats don’t—but most inexpensive rubberized bases break down over time, especially in heat or humidity.

The culprit is plasticizers or low-grade adhesives that migrate into the wood finish. Once that happens, removal is a pain: goo-gone, isopropyl alcohol, patience, and maybe a gentle plastic scraper. No scraping with metal.

If you must use a rubber pad on a nice wooden desk, put a piece of felt, a thin cloth, or a glass sheet between the rubber and the wood. Or just skip the mat altogether—your mouse doesn’t need one anyway.