According to this article, there is a very concrete, neurological link between empathy (the ability to identify with other peoples emotions), and the tendency to imitate others.
A team at the University of California has conducted an experiment that used Magnetic Resonanced Imaging (MRI) to measure brain activity in subjects who were either observing other peoples facial expressions or imitating them. The areas of the brain stimulated by these two activities were found to be similar, but when the subjects were mimicking the expressions, there was an increased activity in the parts of the brain responsible for regulating emotions.
From the article: Even if someone has suppressed most of their ability to empathize, Iacoboni says, anyone can become more empathetic. “If you want to become more empathetic, you have to try to look at how people act and move their body and their face. Try to mimic it a little bit, and you will feel internally what other people feel.”
This seems to validate one central tool of NLP, which is to create a rapport between the practitioner and the subject, by mirroring the subject.