I've personally shot Provia 100F at EI 320 (1/3 stop slower than 400) and had it pushed 2 stops. It came out pretty well. Definitely a contrast boost, and better suited to indoors with flash than outside on a bright sunny day, but there was definitely something there.
If the OP or a lab was willing to push 3 stops, there would definitely be *something* there. Pushing slide works far better than pulling slide film, IMHO. In my experience, highlights still get lost when pulling slide film.