It depends in what you are interested in measuring - the amount of noise in the image (all else being equal), or the amount of noise in each pixel. Sensor technology is sufficiently advanced so that the biggest determinant of noise is pixel size. It comes down to the number of photons that can get into the pixel well in low light conditions - it's a fundamental physics problem. Big pixels will always exhibit less noise than small ones. That's why full frame sensors have better low light performance than smaller ones - because each pixel is bigger than it would be if you crammed the same number of pixels in a smaller space. Conversely, if you cram more pixels in the same space, each individual pixel will be noisier. The catch is that by downsampling you are creating bigger "virtual" pixels by combining smaller ones.
I think downsampling a D800 image to 12MP is fair for comparison if you are interested in comparing the final image. If the question is whether final images from a D800 will look as good, or better, than those produced by a D700 when printed to the same size - then the answer is yes. If the question is whether a single pixel will be noiser (a useless comparison, in my opinion) then the answer is probably no. After all, what is it we are producing with these cameras - images, or something else?