No internet access would be hanging up the AutomaticUpdater. All the downloading, checking, and updating is done by wyUpdate.exe. The AutomaticUpdater just talks to wyUpdate to tell it what to do. So whatever is hanging up your form it's not caused by internet access.
That being said, wyUpdate does access wyday.com for self-update access. You can always host wyUpdate yourself if this is a problem.
But you'll need to install a debugger (or at least reproduce this problem on another computer) to diagnose the hang.