Don't expect "natural" colors or normal contrast if you underexpose and push any film, especially two stops. Doing this always raises contrast and affects color. It is still worth doing it to get a shot, IMO, though it does depend on the criteria for the specific application. It is better than no shot, but you need to recognize that this contrast boost and color change is going to happen. For an underexpose/push to work, the contrast physically has to go up.
You are better off using Provia 400 at 800 IMO. It is inherently flatter, so a one stop underexpose/push does not raise contrast as much as a one stop underexpose/push of a more contrasty (i.e slower) film. Also, that way you only have to push one stops, and will get closer-to-normal color.