This is absolutely the question of the day. The answer of the day is of course, yes you can. You know, I wish more people would do this. The problem is that not many people are thought of how or why they would do this in the first place.
I remember that when I was in high school, my teacher used to have me sight sing my music. I would sit on the bus and literally say every note that was written on the page. You can do this for both treble and bass clef. You can also practice your rhythms by simply clapping them out. If you can have a metronome when you do this, it would make it even better. Just don’t annoy your friends, family and neighbors too much.
Listen to your favorite radio station and try to identify different interval distances. The more that you do this, and relate it to the notes written on a page of your music, the better your ear will develop.
Why not try and learn some history by reading about famous composers and pianists. As long as you are studying the instrument, you might as well learn every aspect of it.
One of the final things you can do is to read some theory books that explore scale writing and harmony.
I could go on and on. Musicians have to develop a curious mind with respect to their profession. Provided you have reliable sources and resources, you can find out so much useful information on your own.
Point number one and two are especially crucial in a pianist’s development. The faster you can identify notes and rhythms, the better you will read music.