I wouldn't.
Most commercial bathrooms use disposable towels made of paper. Paper products will scratch the finish. A few upscale establishments use real fabric (terry cloth) but these are likely to be polyester-cotton blends (cotton for softness, polyester for strength and durability), which may also scratch the finish. If they're real fabric, you'll see a separate container (in addition to a garbage can) for the towels, so that they can be washed and re-used.
The long-time recommendation by professional car detailers is to use 100 percent cotton products ONLY, and this has been supplanted in the past few years by recommendations for microfiber towels. Either is likely to be better for the finish than something found in a commercial restaurant's rest rooms.
P.S. This is a topic in which comquat1 has the expertise!
P.P.S. I don't condone stealing bathroom supplies from restaurants. Regardless of whether or not they are good for your car. Calling something you steal "free" is shameful.