Deal, I have a 32 GT-R that i'm just beginning to modify for a little bit of track work I like the whole regular street driven occasional track car thing and a GT-R is almost perfect for those duties, if you keep it sensible and do as much of the work yourself as possible then I think its possible to get away with a reasonably quick car for a reasonable dollar.
Another thing to consider is that the advantage of the GT-R's AWD system or that of any AWD over the RWD is directly proportional to the power output of the car that is, its a bigger advantage the more power you run generate.
This is not to say that there are not high powered real wheel drive cars out there, because any one who tells you that is having a good pull on your leg, just have a look at some of the guys in this thread.