They do, and you should clean droppings off as soon as possible. Bird droppings can be acidic or alkali and also contain grit and bacteria. Once they start to harden, real damage is being done. This toxic mix reacts with the paint surface, making it shrink. It leaves dull patches in the paint that are extremely difficult to fix. If you didn't get it off before it hardened, soften the spot by leaving a damp cloth over it for 10 or 15 minutes, then carefully clean it off. Avoid spreading the mess further. It's best to dispose of the cloth – bird droppings really are that unpleasant.