But does the mini require a persistent connection to play single player games?
According to this new rumor, no.
Xbox Mini as a standalone device is good for TV functionality and downloadable gaming content, only combined with the Durango can it play disc games, via the Durango disc tray.
it would require a network connection and internet to provide any real functionality.
You will need it as online as you would need a X360 without disc tray. It won't block you from playing without internet, and you can't place any game there without a connection (or a Durango linked).