Yes but the current position of all 6 motors is not enough to determine the state of all 26 cubes. Tracking moves with an encoder for each motor (which you want anyway to ensure you didn't overshoot on a move) sounds like the way to go.

I imagine theres some protocol to tell the controller the cube is solved (e.g. only turn it on in a solved state) and it just tracks moves from there to determine the current state.

That's how I solve a partially solved cube when I pick them up -- just look at where it is and what's next, don't worry about how it got there.