Without a fuel, there is nothing in the cycle that would really accelerate the flow through the engine. You have to have some kind of energy source.
You wouldn't want to play around with gasoline in a turbine. It has a tendency to explode. It's too volatile. The fuels arena is a very active area of research. The current state of the art really has different fuels with different energy contents and operational parameters to allow the particular vehicle to operate in its required regime. It does play a role in overall efficiency. However, like the internal combustion engines in cars, one runs into the same problem of finding anything better in terms of energy content per unit mass of fuel.