Daniel Keller of Keldan Lights has published a video showing how filters effect the way cameras record colors underwater. Utilizing a side by side rig with two Canon 70D, one equipped with his Spectrum filters and the other one without, it shows that filters will help achieve more pleasing colors than can captured by using camera white balance alone.
Daniel found that the affective complete absence of red below about 18-20 meters (60-65 feet) means that many cameras will either fail to achieve a white balance, or produce one that is inaccurate. In order to address this, he suggests that filmmakers do not try and white balance below this depth, and that the best results are achieved by “holding” the shallower setting at greater depths.
This graph shows how a filter essentially extends the color rendering and actual color spectrum (co ordinates) through the depth range. By adding one, the spectrum at around 15m (50 feet) gives a similar results to using white balance alone at 5m (16 feet) or so.