Do you know if the ACE storage battery is part of the AD?
No, but I do know that ALL Li-Ion batteries were disconnected by at least one airline when they were grounded in January. Which included the ACE battery modules.
To my knowledge, the Ship's and APU batteries for the 787 power the same systems as they do on other Boeing Commercial Airplane families. So I don't believe Boeing is asking more of them on the 787 than, say, the 777.
Except of course the emergency and towing brakes systems. (Main bat only).