Yes and no and it's complicated.
People will occasionally attempt to colour-balance their strobes with the ambient light by placing blue or blue-green filters over the front of the strobes. The effect this will have is that the parts of the photo lit by the strobes will have the same colour cast as the shadows (which are lit by ambient light), rather than having natural-coloured strobe-lit areas and extremely blue-green shadows. You would then either set your camera's white-balance or use a camera lens filter (such as a
magic filter) to remove the colour-cast from both the strobe light and the ambient light.
This is rather difficult, so the vast majority of UW photographers will just use dual strobes to light everything the camera can see with white light. (Far from a perfect solution, but usually good enough.) For the minority that do attempt to colour balance their strobes, I think attempting to adjust the colour of a strobe underwater (as opposed to just attaching a filter for the whole dive) would prove too difficult. I think the only way a colour-controllable strobe or video light could work would be if it could automatically detect and match (or partially match) the colour of ambient light.