They don't have a "centre diff". They have a transfer case which sends some drive to a front differential (hangs off the side of the sump).
GTT doesn't have a front diff and transfer case because it's not AWD (?). I suspect you are talking about the rear diff (which is located in the "centre" of the axles). GT-Rs, AFAIK, have a 4.111 final drive (diff) ratio. Stageas run 4.083 . R32 GTS4s run 4.375 . Don't know about the GTT.
But, yes, the GT-R diff should fit into the GTT.