Then it still has nothing to do with a Domain Logon, and nothing to do with Cached Logon which is for the credentials.

I'm sure one knows if his/her logon scripts are being run locally or from a Domain.

In most cases even if you had the executable and the scripts both on the local work station they are typically called from the logon process of the Domain, not locally so it still would not run, unless you setup to run in the registry or the startup group. But then anything you tried to do like writing logs or stuff back to the Domain would fail. You could then add code to write local logs, but you still wouldn't know as an Admin when the user was local or on the Domain.

The whole process of trying to do logon scripts locally sort of defeats the purpose of easy workstation management.