There is very little benefit to installing an aftermarket downpipe without a tune. It is unlikely that you will notice any improvement.
While SD is correct, the 2002-2003 WRX seems capable of supporting a TBE with no tune and few detrimental effects. However, a downpipe is a performance part and the car should be tuned accordingly. Any part that changes the airflow and/or fuel dynamics of a motor should be tuned to extract the full potential of that part.