Negatory. USDM MY04-5 WRX rear diff has a 3.54 ratio while the front diff is 3.90. The transmission includes a 1:1.1 transfer gear connected to the center diff that only affects the rear driveshaft.
If you're going to use a USDM WRX rear diff, you have to get a new R&P. Otherwise, you can source a USDM '91-'93 Legacy Turbo rear diff, which is a 3.90 R160 (some with viscous LSDs). Somebody on NASIOC also supplies what I think are JDM 3.90 R160 units (SpecC4U (?), a vendor from Canada, IIRC).
Interestingly enough, the MY08 Spec B comes with this 1:1.1 transfer gear in the 6MT, too (according to the service manual). The rear end is an 3.54 ratio R180.