Sajid requested I open a new ticket for this unexpected behavior with the Pro Sites widget module. FYI: The issue seems similar to this topic regarding ads displaying on Pro Sites that has now been resolved.
The Pro Sites Widget is only displaying on Pro Sites to logged in users. No Widget displays on Pro Sites to the public, if not logged in. I have confirmed this on two different installs.
See attached screenshots for detail, or visit these sites on our dev install to see for yourself. Support access has been granted.
Pro Site Level 1
Pro Site Level 2