Want to know when you have a good connection between your Local Computer and your Domain?
Might I suggest Test-ComputerSecureChannel to you?
The Test-ComputerSecureChannel cmdlet verifies that the channel between the local computer and its domain is working correctly by checking the status of its trust relationships. If a connection fails, you can use the Repair parameter to try to restore it.
It seems to take about 10 seconds to establish that connection, so if you think that it would be useful to use in a logon script, you should look elsewhere.