You could. The output splines on the input shaft is the same IIRC, so the diff itself should work, and using the transfer gears from the STi would probably work as well.
It'd be expensive, though. The diff alone is $2k from the dealer, and finding used ones that aren't broken is time consuming. And you'd need a DCCDPro controller, of course.
VDC wouldn't care at all.
Driveshaft should be the same as the stock 6MT Spec-B unit.