Can hydrogen gas be an alternative fuel source for a gas turbine engine?
Yes, and it has been demonstrated 30 years ago on the Tupolev 155. This is/was a hydrogen-powered version of the Russian Tu-154B tri-jet. Only one has been built and has since been retired after demonstrating the use of liquid hydrogen in 5 experimental flights. In total, the Tu-155 performed about 100 flights with several fuels, among them hydrogen and liquefied natural gas.



Tu-155 (top), cut-out (center) and layout (bottom). Source: https://www.aviaru.net/pr/?id=11633

Hydrogen is actually better for a jet engine: It is gaseous at normal temperature, so there is no delay for the evaporation step to happen as there is for liquid fuels before mixing and combustion can start. Also, hydrogen burns in a wide variety of mixing ratios with oxygen, so flame-outs are much less likely, making a smaller combustion chamber possible.

The downsides, of course, are storage and the small molecular size of hydrogen. It is very hard to contain, and it needs big volumes to store a given amount of chemical energy. Pressurized storage at 200 bars holds only 18 kg/m³ or 45 times less than kerosene. With 142 MJ/kg, hydrogen holds three times as much chemical energy than kerosene, but then the volumetric efficiency of kerosene is still a factor of 13.3 better.

Cryogenic storage swaps pressure for low temperature: Below 33 K and above 13 bar, hydrogen becomes a liquid and storage density increases to 30 kg/m³. Still, cryogenic hydrogen storage needs 4 times the volume of the same amount of energy stored as kerosene, plus the isolation and the energy to cool it down and compress it.