Yes, it can damage a number of things, but often it does not do any damage. I suppose this is the hazard of using chemical cleaning methods on any bicycle. Beyond what has already been mentioned about decals and rust under paint/plating, remember that certain makers also used primers and paints containing rust/oxide compounds. This was often true of red and brown paints and primers. If the paint or primer has enough of an oxide component, the acid may lift or distort the color of the paint/primer. However, some of the reds/browns don't contain enough oxide for the OA to harm them, while others are either removed or their color badly distorted.
Test the OA on a part of the bike that will not be obvious before treating the whole thing.