Hydrogen Fuel Cell Spacecraft?

To any engineers or knowledgeable amateur enthusiasts: would it be possible to build an SSTO that uses hydrogen fuel cells to generate electricity to power an on board beam propulsion system (like microwaves or lasers)? This would use air as the propellent and hydrogen for the electrical generation (obviously). Or would such a system be monstrously inefficient? That is would it be more efficient to directly convert hydrogen and oxygen to thrust as is the current convention? I crunched some basic numbers and it seems that enough hydrogen to equal the energy production potential of a small nuclear reactor over a small but practical amount of time for an engine burn could easily fit within a 500-1000 imperial ton type of launcher with a very high payload to fuel ratio. Of course I'm probably way off and that's making a big assumption that the equivalent of a small nuclear reactor would produce enough energy for the task at hand. On an unrelated note, I used A LOT of run on sentences in this post, but thoughts are appreciated!