So am I correct in saying the alternator stops producing power when the ignition is turned off regardless of the engine still turning?

That's about it. As the exciting current from the demand in the system is shut off by switching off, then so too does the output from the alternator. There may be some residual magnetism in the rotating alternator, but not enough to do any harm for the few rpm remaining. (He says - without an electrical hat in sight . . .)

yes, I agree with that statement. BUT if I cut the battery out before the ignition is turned off, that would be another question! In effect, the alternator would be feeding the ignition circuit and the alternator regulator. The power from the alternator would have nowhere to go and would probably frazzle something ?
BobH

Agreed, so don't do it then.

Could you explain to me, the purpose of the cut off you have and how it functions.

Roger, since this switch doesn't have an alternator protection feature, isn't it really just a 'battery isolation' switch?

Ken, I don't know, that's why I was asking.

What's its point, how does it function?

Battery isolator, cut out switch - just about the same in my book, but as ken says, there are switches with alternator protection as discussed earlier in this thread. The purpose is to prevent a fire from an electrical circuit fed by the battery when the engine is at a standstill, either a circuit where a component has failed and shorted out to earth, or wiring which has chafed and shorted out to earth. A fire is probably the next worst thing that can happen after a collision and in many cases can be the end of your 'pride and joy'.

If you eliminate the battery, then it is impossible for an electrical fire after you have parked up. Well nearly impossible as the impossible is always possible - Said the Camel to the eye of a needle.