Depends upon the lab, since not all labs want to do this. I was given some of the Portra 800 by the local Kodak reps just to try out that way, since they know I do crazy push processing with E200 (transparency film). My comparison basis was more to an older film called Ektachrome P1600, which can easily be used at ISO 6400. So after a test, the Portra 800 worked better than the old P1600 (transparency film), because I felt it had less grain and less colour shifting.
I did not feel it worked better than E200 pushed 4 2/3 stops, though I will admit that the Portra 800 was easier to use and more forgiving of exposure (as one might expect from colour negative). The other negative factor for me is that the primary lab I use has to ship out my film for push processing Portra 800, but can easily do the E200 there.
So check with your lab first. If they don't understand push processing C-41, then the bad part is they might just try to make prints off your one or two stops underexposed film . . . that would be really grainy.
Ciao!
Gordon