Can a MOSFET be on if there is no current flowing through it?
When talking about a MOSFET being on or off the only thing we consider is the gate-source voltage Vgs. If Vgs > Vt then a conductive channel is formed between drain and source resulting in the transistor being on.

This is unrelated to the fact if there is actually a voltage across drain-source or a current flowing between drain and source.

Compare it to a mechanical switch with an on position and an off position. Even if you do not connect that switch to anything (you hold it in your hand, it is not mounted in a wall) it can still be in the on or the off position. But only if it's in the on position there is the possibility that a current can flow when the switch becomes part of an electric circuit.

Same here, although M6 is on no current can flow as M2 is off, blocking any current flow.