Yep, A8DH200X, A8DH201X, and A8DH202X roms are all cross-compatible for the 06 USDM WRX that use the ecu marked '22611AL350'.
However, you will need to have the car towed to a dealership/shop with SSM3 diagnostic tool (or have them come to you) to have the new ECU paired with the immobilizer and your keys. That will run ~100 something depending on the dealership and you will need the key code that comes with your keys (small plate with etched numbers). It's something like $50 for the dealer to look up the key number if you lost it.