Mechanically it's possible, since the GT-R itself is loosely based upon Nissan's FM platform which underpins everything from Infiniti's sedans, to SUVs, to the 350Z. Modification would involve the stretching of the platform to accommodate the larger rear seats and doors. Hard points would be shared with the coupe.
Mechanically, the cars should be identical, though the rumors also state that the sedan version may be offered as an Infiniti, meaning different styling and the loss of some of the trick carbon and other go fast bits.
Our take? Anyone who's played Gran Turismo knows that fast 4-door Nissans are nothing new. Previous 4-door versions of the Skyline (GT-T to be exact) had turbo I-6 motors just like their GT-R brethren. Really the biggest differences were the lack of 4-wheel drive and trick chassis electronics.
Still though, don't be surprised to see a full fledged four-door GT-R. Infiniti made a big stink originally over not getting the GT-R, this would do much to appease the brand.