Technically, yes it should work, but you would have to re-assign all the buttons (in the Settings/Controls window) I think, and also possibly use a 3rd party app like DS4Windows, from what I read.
However, currently I don't own a PS4 controller, but at some point will be getting one to do testing with as I would like to make it more easy to use PS4 controllers and/or make sure it works 100%.