Nope.

That wire grounds the ignition - which prevents the electricity from jumping the gap in the spark plug. So in a one-switch setup, the switch must be closed (ON) for the engine to QUIT - which is backward from the way you would normally think.

You are talking about hooking them up in series. In series, they must both be closed (ON) for the engine to quit.

You want them set up so that if EITHER one is closed the engine will quit - so you want them set up in parallel