To say it can is to say it’s possible. Considering the wide range of artistic expression and the amount of art throughout history, I believe it is not only possible but very probable that art be one of many factors that can influence a person’s sense of self.

An hypothetical example:

Suppose you are contacted by a historian and agree to meet with him. The historian presents you with a painting by a very well-known artist. The historian says that it was discovered that this artist has a journal where he mentions your great great great grandfather as being the sole inspiration for the painting. In the painting, the historian points out a person in the background who bears striking resemblance to your mentioned ancestor. You then remember how often your relatives say you strongly take after your great great great grandfather.

I would think that if this doesn’t influence a person’s sense of self then it’s not a measure of arts inability to influence but a measure of that person’s apathy.