Distortion can cause problems in a n-way speaker because the distortion components can be passed by a crossover and end up in a high frequency driver not designed to handle large amounts of power.
I think speakers don't know and don't care if a signal is distorted or not. They just reproduce what is sent to them, no more, no less.
In fact, you can be certain that signals without any distorsion don't exist.
Sending too much power to a speaker can damage it; distortion does not damage speakers, it only muddies the sound.
If you'd like to check if distortion damages tweeters, get this file:Thomas Edison - Great Speeches - 1887, First Gramophone Recording Ever.mp3
and play it on your system. The sound is very distorted so it should make a very good test.