I like the idea of everything being GFI protected, but it's not required by any codes I know of... Mike (jwelectric) is the code expert, though: wait till he confirms/denies this.
Even if it wasn't overloading the box (and I think it would be), I just don't see how you could physically fit 4 runs, the required wire nuts, and a GFI in a normal receptacle box.
I've come across this sort of problem before, though. My sparky uses a larger box:
http://electrical.hardwarestore.com/14-45-electrical-boxes-metal/square-box-239574.aspx
(you can also get extra-deep version of this, if you need even more room inside)
With a mudring on it:
http://electrical.hardwarestore.com/14-45-box-covers/4-square-cover-raised-1-4--662552.aspx
The mudrings we use have a bit more depth on the raised ring. He installs them so that the ring's level with the wall finish surface, and I plaster/tape over the sides. You can still get to all the wires from the opening, so it's not a concealed junction box.
Side-note: you want to leave your wires, in the box, longer than the usual 6". He usually leaves 9 or 10, for this kind of setup.
BTW, overhead lighting in a bathroom really sucks when you're trying to shave, because of the shadows.
Mike can tell me if this is legal - I've seen it a lot, in old work - could you run the light off a receptacle box installed sideways? Then it's only about 2" tall, and you'd have room between the pipe and the cabinet. Since all your junctions would be in the receptacle box, capacity wouldn't be an issue...