Generally speaking, you can't mix high voltage (120, 240 and above) with low voltage (definition varies, but 24V is definitely low voltage). This means you can't use part of a high voltage cable for low voltage DC, and it also means you can't mix and match low & high voltage individual wires in conduit.
Part of this is the obvious "accidentally bridging the 24v +DC and AC live" safety problem, and there are other reasons as well.
As far as the specific question of neutral or ground as the other 1/2 of the circuit. No, you can't do that. Along with any other safety issues, the wires have fundamentally different uses:
- "Ground" in DC circuits refers to a return path for the circuit. The "ground wire" in a mains AC circuit (the green or bare wire) is not normally used to carry current, except during a fault situation. Loading it up with 24V DC is therefore not a good idea.
- Neutral in AC circuits is logically like ground in DC circuits, but it actually carries just as much current and the AC variation thereof. So some of the time that DC current would (theoretically) be opposite the AC current in the neutral (i.e., bringing it closer to 0) and some of the time it would be in the same direction (more current than normal). In any case, it won't work and it isn't allowed.