I could still be useful as a propellant for say, a nuclear thermal engine.

Unless you can fuse it into helium.

If you have the tech to fuse hydrogen the amount of fuel you would need for a nearly unlimited amount of energy is tiny, you would save very little by harvesting it off a comet/asteroid.

Depends on how much energy you need. If you are talking about turning it into an interstellar spacecraft by hooking up some kind of fusion powered thruster (probably using H2 as the reaction mass) to the back you may need all of its mass.

This is of course well beyond our current capabilities, but it's not something that's impossible to consider in the medium-distant future. Plus, even if you expend a colossal amount of energy accelerating you're still talking about thousands of years for the journey where you'll need to keep those reactors running for the entire trip (there is no useful solar collection in deep space) having a literal mountain of fuel to start with is important.

Unless you just want to colonize this hydrogen iceberg, and live on it for next thousand years, recycling all other elements indefinitely as you cruise through the galaxy.

You still need propellant mass. Energy in itself doesn't get you anywhere. But in practice you'd probably be better off electrolyzing water ice which is ubiquitous in the outer Solar System.

Insulating the fusion reactor from the solid hydrogen in Oumuamua could prove difficult.

Put Oumuamua at the front? It's not like drag is a concern.