Can sulfur dioxide bleach damp litmus paper, like chlorine does?
Most likely, yes. Compounds that “bleach” dyes can do so by either oxidizing (as with chlorine) or reducing (as with sulfur dioxide) the coloring matter in question. Sometimes the coloring matter will be resistant to being oxidized or reduced, or both, but based on the structure of the dyes that make up litmus, it looks like it could be easily reduced. The best way is just to test it yourself! Any “bisulfite” or “metabisulfite” salt or a “sulfite” with a little acid added to the solution will work the same as sulfur dioxide.