I had meant to post a follow up to this a while ago but forgot about it.
I ended up opening a support ticket with VMware and this is what they told me to do which fixed the issue:
On the master image, go to the following key in the registry: HKLM\SOFTWARE\Policies\Microsoft\Windows\NetworkConnectivityStatusIndicator
Delete everything but the (default) key
Reboot the master image and test Outlook.
Once I did this, I refreshed the desktop pool and all was good again.
