My wife and I were playing again last night and this came up. It seems that they can but we would like some clarification.

If an event with a proper interrupt is in your hand then yes.

For events that play like an action the answer is no. There is no action window in the midst of an edge battle.

There is only one event (interrupt) that currently works during an edge battle:

Reversal of Fate

Nothing else, yet, has text that allows playing during an edge battle... note, though, I'm not including things like Lightsaber Deflection and others that can interrupt and redirect damage during the resolution of said edge battle.

Learning has occurred.

Ahhh....The flow chart on page 30 means something! Thank you both.