No you don't. That would happen if the operator continuted to crank and pump without it starting. If it had a bad coil, and the throttleman operated/started the car correctly, a bad coil would net the same results as when the key is turned off.

Anyway, that't the way I would troubleshoot the problem, and I have established myself as one of the cheaper members, not buying anything I don't need. If you want to follow another game plan, by all means, don't let me influence you. It's a proven fact around here that I don't know jackshit about anything.