Kodak does not mention push processing in their Portra 400 instruction PDF, but they do state "No increase in development time is required for a 1-stop push." in their
TMAX 400 instructions. This basically means, that an 1 stop push is handled by the latitude of film and adjustments during printing. Extended development would increase contrast and grain, and gain little to nothing in the shadows.
PS: Whether you can shoot this film at EI400 or at EI6400 depends to a great degree on scene brightness ratio and your metering technique. Are there deep shadows with necessary subject matter? Do you measure darker areas, average brightness or into highlights? Or do you just shoot at what the (more or less intelligent) metering system of your camera says. If you measure shadows, then a shot @EI3200 will look great, whereas if you measure highlights, even EI400 will give you underexposed negs.