Here is an example of another video that may look pretty bad due to auto wb being off using a GoPro HD hero2 and URPro green water filter. I got this video off youtube and used my Colorista 2 Pluggin for adjusting the wb using his slate and dive computer as a white reference point.
Because this was recorded with a filter there was still more colour detail captured compared to shooting without a filter or lights. I only had a youtube encoded source file to work with so there would be better results if this was done with the original footage. Unlike your example though the footage isnt lost because of the filter being used and all you need is to correct the wb and you will get a much better result.
The water is pretty murky green here and vis/light isnt great but its still amazing what this little plugin can do and I use this for all my underwater colour correction. I have shot other GoPro videos myself without a filter and this method doesn't work beyond about 4-8m because it simply didn't record enough colour detail. Combining a good quality filter and software correction will give you the best results.
Here is the original video, this was uploaded as is with no colour correction.
[video=youtube;alQMirzB5no]http://www.youtube.com/watch?v=alQMirzB5no[/video]
And some screen grabs I corrected from the video above. Using Premiere Pro and Colorista 2 plugin.
I tried a few methods until I stumbled on to the Magic Bullet Colorista 2 plugin and it can be so simple but also very powerful if you need more. I highly recommend anyone to try this plugin especially if you have a camera with no manual WB control and are using a filter. All you need is to shoot a regular white point like a slate or even a mid grey as in the dive computer here and the pluging will give these sorts of results with just one click. You can then fine tune any other possible option to do with colour if you feel you need to do a little bit more.
Red Giant - Products - Magic Bullet Colorista II
If you had a camera that could record video in RAW mode then you would get the best possible results, gopro's new Protune firmware is moving towards a more "RAW" cine style higher bit-rate format which will make this work even better for anyone that has a Hero2 camera once its released.