No, generally speaking, waves pass underneath a floating object in practically all circumstances. You may feel like there’s a forward surge when a wave comes in from behind, but all forward momentum gained while sliding down the wave is lost once the wave peak has overtaken you and you’re climbing back up the wave. Basically, waves will induce a circular motion on a floating object.

There’s ways to trick and gain forward speed from waves, by basically picking a wave that’s high enough and continually sliding down on the front - Surfers for example. But that only works if your object is substantially smaller than the wave in question - which is sort of impossible for ships.