It's true that the ignitor, sometimes called the ignition module, could cause the car not to start.

If you suspect the ignitor you can follow the steps in a repair manual and do tests on the ignition coil reistance, power from the ECU, etc. so you can rule out everything else.

However, the ignitor itself going bad wouldn't prevent the battery from being charged by the alternator or cause the battery to drain overnight - requiring it to be jumped the next day.
If there was a problem with the distributor or anything under the distributor cap, even the cap itself, the starter would still crank the engine even if it wouldn't actually start.