Probably not with your existing guitar. jonny mentioned MIDI transmitting and he's right. There are certain pickups for electric guitars (like Roland's GK2A MIDI pickup) that let your guitar transmit notes not as the normal electrical audio signal, but as MIDI data (i.e. "play such-and-such a note at such-and-such a velocity and hold it for such-and-such a length"). Your computer (or any other MIDI synth device) could then take those note instructions and play them back, but through a different instrument sound (piano, organ, synthesizer, etc.). Overall, it's a lot of hassle and doesn't always work that well.