From the Hydrogen economy
article on Wikipedia:
There have also been some concerns over possible problems related to hydrogen gas leakage. Molecular hydrogen leaks slowly from most containment vessels. It has been hypothesized that if significant amounts of hydrogen gas (H2) escape, hydrogen gas may, because of ultraviolet radiation, form free radicals (H) in the stratosphere. These free radicals would then be able to act as catalysts for ozone depletion. A large enough increase in stratospheric hydrogen from leaked H2 could exacerbate the depletion process. However, the effect of these leakage problems may not be significant. The amount of hydrogen that leaks today is much lower (by a factor of 10–100) than the estimated 10–20% figure conjectured by some researchers; for example, in Germany, the leakage rate is only 0.1% (less than the natural gas leak rate of 0.7%). At most, such leakage would likely be no more than 1–2% even with widespread hydrogen use, using present technology.
 ^ a b "Assessing the Future Hydrogen Economy (letters)" (PDF). Science. 10 October 2003. Retrieved 2008-05-09.
The implication there is that even if leakage were a major problem, the gas doesn't escape the planet. Even if it did, and we switched entirely to hydrogen, and consumed 100 times the current rate of energy, I have a hard time believing we'd actually make a dent in the oceans. I'm going to guess that, by volume, the amount of oil that was ever on the planet is pretty trivial compared to the size of the oceans. Unlike what happens to oil when we burn it, most/all of the hydrogen would eventually be converted back into water.