Yes, sandpaper can damage porcelain tubs. Porcelain is a hard, non-porous material, but it can still be scratched by abrasive materials like sandpaper. If you use sandpaper to clean a porcelain tub, you may end up causing permanent scratches that will dull the finish of the tub and make it more difficult to keep clean.
If you need to clean a porcelain tub, it is best to use a non-abrasive cleaner and a soft cloth. You can also use a baking soda paste or a vinegar solution to clean the tub. These methods will not damage the porcelain finish and will help to keep your tub looking its best.