Consider James Young’s color theory. Combining selected colors of light will result in white light (5,500 deg. K, mas o minos).
It will produce a metamer of white light. Such a combination appears white because of the limitations of our vision. "White light" is full spectrum and is not composed of selected colors.
Consider water a defusing, dichromatic filter. The greater the distance form your light source (strobe) the more the color of the light is changed. With R then G and then B being most affected in that order.
There's a lot wrong with this explanation but it doesn't effect the discussion any. The most important correction that I would make is that filtered light is not predominantly blue; it is cyan to green and it varies with water quality.
Adding Y to your camera lens will affect the Sun lit water background (ambient).
A lens filter will effect all light entering the lens including strobe light as well as ambient. For digital cameras, a lens filter should be thought of as a supplementary white balance filter that effects the image before the exposure (and thus preserves the full performance of the camera sensor). Lens filters work on full spectrum light where as white balance works on an RGB color model.
Adding R to your strobe(s) will increase the R in your illuminated foreground. With E6, I would get deeper blue water by simply metering the ambient water background and reducing the exposure 1 to 1-1/3 stops and adjusting the strobes for proper lighting. Craig, I am disagreeing with you on this point: I am assuming that the strobe lighting would not over power the ambient lit background.
Your E6 background is insufficient for this discussion. Digital allows you to white balance to your foreground light source. Film does not. You would never filter your strobes away from white with film unless you wanted a special effect. Putting a red filter on a strobe and recording the image with E6 will simply result in reddish subjects.
Film, on the other hand, is highly non-linear (unlike digital) so other techniques such as you describe may change the hue of the water. With digital, reducing background exposure results in darker water but not bluer water.
With the previous disclaimer still enforced, it seems to me it is easier to color correct (RAW, digitally) post exposure than to be committed to and absorbed with color correction while composing the initial image.
That's simply another argument claiming that postprocessing is preferrable to a lens filter and has been covered repeatedly. Strobe filters alter the color balance between foreground and background and their effects cannot be duplicated by postprocessing. It may be difficult to see how a strobe filter effects background color when your experience is with film since with film it does not. With digital, any strobe filter automatically comes with adjustments to white balance in the raw converter. White balance with film is fixed.