After a Surprise Defense is initiated, can Shen be played as an extra defender during the combat there?

No. During a Surprise Defense, the battlefield remains Uncontrolled because control is only established at the end of a non-combat Showdown. Since Surprise Defense creates a Combat scenario (not a non-combat Showdown), control is not established during this phase. Shen requires playing to "a battlefield you control," so he cannot be played to an Uncontrolled battlefield during a Surprise Defense.