OK, I stopped the test because I was getting bored and the camera wasn't near dying. Here are the results:
GoPro Hero 3 Black Edition.
46-54 degrees F
0.8ft depth
1440p 30fps protune mode
Camera on entire time, shooting 30s-4min chunks: camera auto-shutdown: 2 hours, 19 minutes. Total video captured: 19 minutes.
Camera one-button mode (off between shots), shooting 30s-9min chunks: camera shutdown: N/A (went down to 1-bar, which is about half battery life, at 3 hours 1 minute). Total video captured: 39 minutes.
Again, for me the results are pretty clear cut. If you want preserve battery life and you're shooting a fairly small number of short clips, turning the camera off between filming is the way to go. I imagine this test is wholly irrelevant if you're shooting for the entire dive, or if you shoot several hundred 5-second clips per dive.