The answer is both yes and no. Yes, if you use them the way they are supposed to be used, and no, if you use them in excess or don't follow the instructions. The ingredients used in teeth whitening are known to be safe, if used in proper quantities and in the right amount of time.
But, using these same products without proper supervision from a professional dentist can cause some people unnecessary harm. It's therefore always advisable that teeth whitening products be used under proper supervision from professionals. Failure to see a dentist or consider your overall oral health can create side effects such as heightened sensitivity.