They do use the same hydrogen as Dropship and fighter reaction mass.
More important though is that any fusion plant can extract hydrogen fuel from available water sources, so a fuel cell equipped force can always resupply from its dropships as long as there's a convenient and large enough body of water.
So availability of fuel isn't really the issue, but getting it to where it needs to go is. And since fuel cell vehicles burn fuel faster (have a shorter range for the same fuel fraction) then you either need a larger logistical tail supporting you, or you have to advance slower on the strategic scale (since you have to stop for resupply more often).
Alternately, you can mix fusion powered vehicles with your main force to handle fuel production, but that still depends on having enough water on hand, and it raises the total costs to a point where you might start wondering why you didn't spend the extra to go full fusion so you didn't have to worry about moving fuel around.
Seriously, it doesn't come across often due to the scale of the game, but there's a serious advantage to using fusion power and not having to worry about tanker trucks.