It's not a coil, it's a magneto. No, no power goes to it.....
EVER. The white wire is a ground wire. It runs to the key, (by way of safety switches) and when in the off position, it grounds the wire and kills the spark.
If it has no spark either:
1.) The mag has failed
2.) There is an issue in the "OFF" circuit, and the mag is constantly grounded.
You can disconnect the white wire at the mag, or at the connector on the outside of the engine and check for spark.
NOTE: With this disconnected, the key will not shut the engine off.