When you push an ISO 160 film in camera to 400, you are under exposing it by about 1.5 stops. When underexposed, pushing the film in developing is usually pretty forgiving so long as you don't overdo it.

What you're effectively doing is telling your meter that the film is more sensitive to light than it really is.

When pushed in the developer, the grain will become more apparent and although the contrast will be greater, the change in contrast isn't uniform across the light and dark areas of the image so the end result won't be the same as exposing it as ISO 160, although it could well look excellent.

If you're looking to experiment with it to see what effects you can create, then you have nothing to lose by giving it a try.

I know a few photographers who routinely push their film for more contrast simply because they like it, however when they need the results to be consistent (such as when they're doing a shoot for a client), they tend to favour a more sensitive film and expose it at the recommended ISO.

One big advantage of pushing an ISO 160 is that with it not being a particularly sensitive film, the grain will potentially be pretty tight which will mitigate the effect of the more apparent grain when pushed in the developer.

That is of course a massive generalisation. Some films are much more tolerant of being under/over exposed than others, so it might be worthwhile doing a little research on the specific film you're using to see if you can find some images which have been pushed.

Personally, I'd give it a try just to have a point of reference, but it's dependant on what you're shooting and who the images are for.

If its your own project, just go for it and see what you think.