My guess is no, since i believe the key fob style has changed between those years, 09 is a teardrop shaped, while I believe 02 is the square shape. When i needed to replace my key fob (06) i found one of ebay for cheap and then reprogrammed it for my car.
1. Unlock all doors
2. Open the driver-side door (My windows were rolled up)
3. Get in
4. Close the door
5. Insert the key
6. Turn it to the ON position (Don’t start the car) and back to position 1, just above the LOCK position 10-12 times within 15 seconds leaving it in the ON position.
7. The horn will chirp
8. Open and close the door
9. Press the unlock button on the first remote
10. The horn will chirp
11. Open and close the door
12. Press the unlock button on the second remote
13. The horn will chirp
Those are some instructions I just found on NASIOC for 03 wrx.