I feel the proposed solution may not be ideal - there's a danger with such automatic features, as users can easily forget such option is toggled on. And generally automatic changes applied by the system should be reviewed by users.
As Christophe described, there might be some edge cases where such automatic archive catch customers that shouldn't be archived.
I personally feel that the user should make an explicit request to archive a customer.
If I understand correctly, the user need is to archive inactive customers. Wouldn't a way to see such customers ('inactive customers report') with the ability to (also bulk) archive them suffice?