That's right about the reactor.
Scott says that they have a main
SCOTT: I can adjust the main reactor to function with a substitute fuel supply.
SPOCK: That's all very well, but we don't have a substitute supply.
SCOTT: Aye, we do. Our phasers. I can adapt them and use their energy. It'll take time, but it's possible.
But I wonder if it was more like the TOS Enterprise's power system where it doesn't generate power but creates fuel for the propulsion pods.
Notice that they lost all their fuel and resort to draining the phasers...
SCOTT: One of the lines gave. The strain of coming through the atmosphere and the added load when we tried to bypass. Yes, that's done it. We have no fuel.
but later on they now have fuel to lift off and the fuel can be ignited so the phaser energy isn't used as simple energy but was converted also into some type of fuel.
SCOTT: He jettisoned the fuel and ignited it.
And here are the lines regarding the batteries being necessary for ignition. I'm presuming it's for the engines (not the reactor).
SPOCK: Mister Scott, how much power do we have left in the ship's batteries?
SCOTT: I daren't use any more. Not and be sure of ignition.