In terms of galactic scale, yes. It is super abundant.
For an example of a world that is hydrogen impoverished, look next door in the solar system at Mars. (though it is also nitrogen impoverished.)
If you want to have a "sustainable" fusion industry, you need to balance the rate of hydrogen consumption against the rate of cosmic hydrogen entering the earth's atmosphere and magnetosphere. (it's absurdly small.)
Failing that, you have to start raining big water ice shipments from space. (and there is only so much out there.) That adds another layer of entropy expenditure though, because now you have all the energy costs associated with an essential space presence.
Nope, really, for geological timescale versions of sustainability, human population must radically decrease.
Egan--
I do not propose "heat death of the universe" scale sustainability-- just "More than a few thousand years, when honestly evaluated against the trend in energy consumption by mankind, with reasonable assessment of entropic losses".
Look at the rate we currently burn fossil fuel for the energy inside. On the order of millions of barrels of oil per DAY. To get similar energy out of fusion, we would be consuming that much fresh water daily to keep the lights on. There is only so much water on the planet.