Close, but not quite. The steel of your engine did not cause your engine to exist. But gravitational collapse of interstellar gas is the process that formed the sun. So, in that sense, gravity comes before the fusion.
It's common to say a car is powered by fuel. It's also common to say a car is powered by its engine. The latter is indeed is a device that brings fuel and air close together (and does some more important things). It's less common, but certainly not wrong, to say a car is powered by combustion.
Similarly, I think saying both 'the sun is powered by gravity', 'the sun is powered by hydrogen' and 'the sun is powered by fusion' is reasonable.