Jag fick ett definitivt svar från forumet Joe Bedurnurn föreslog.
The actual text of the Edge is "The warrior ignores all wound modifiers while Berserk, but cannot use any skills, Edges, or maneuvers that require concentration, including Shooting and Taunt, but not Intimidation."
The free attempt to recover from being Shaken is not the use of a skill, Edge, or maneuver of any sort, so it's not covered. You can attempt to recover from Shaken completely normally while berserk.