Yes teeth whitening has been known to cause nerve damage in some people.
Most people who do teeth whitening at home or have a professional teeth whitening procedure done may experience temporary nerve damage which leads to temporary tooth sensitivity.
However in some rare cases of both at home teeth whitening as well as professional teeth whitening at a dentist the teeth whitening has caused some people permanent nerve damage to the teeth.
When the permanent tooth nerve damage occurs from the teeth whitening your teeth may be more sensitive permanently.
It's rare that the permanent nerve damage occurs from teeth whitening though and I've had my teeth professionally teeth whitened at a dentist a few times and never had any nerve damage although my teeth were sensitive for at least a month afterwards.