Is it Code to support Class 2 (thermostat) wires using a gas line?
Yes it's okay and actually very very very very common. Even the armoured 14 2 cable can be strapped to the gas pipe. Here in Toronto we have the toughest codes around and that's the only way it's done. I'm a licensed gas fitter and electrician. It can't be NMD it has to be armored BX or Tek cable.