If you are speaking of the electrical stimulation like is used in a TENS unit, no, it does not cause any damage to the nerves. The nerves actually transmit electrical impulses.
Of course, the electrical power that we use in our homes, is more than the body can take. And electrical injuries occur if it is not used properly.
But, to just be around a device that uses electrical power is not harmful.
Hope that helps to answer your question.