Yes it does, and it also represents you state of mind at the time you are either playing or practicing. However, above all try to remember what Chopin said, "Play how you feel". This is a quote from Chopin, A Man and his music. Eventhough he use to really get on his students to stay on tempo, he played how he felt. I greatly object to people saying, "this is how you have to play the piece". Bull, it is my interpretation of what I hear and what the composer is telling me through his music.
I will give you a good example. When I starte playing piano my teacher asked me to play any piece of music. So I played Fur Elise. When I was done he said that he had never heard it played that way, but he said he liked it. What I heard in the music was a man pineing for his love. He then meets her and he is over joyed, but they get into an argument and she leaves. He then starts to think about what just happened and ends up bursting out in total anger. But allas he realizes that he still loves her and goes back to pineing for her. That is what I mean by Playing How you Feel. Everypiece of music that you play is yours and yours alone. It represents your personality, so celebrate it and embrace the fact that you have the talent to play the piano. Remember, everyone is a critic.