According to the QRHs for our fleet, this appears to be the case only for A320s with CFMs (MSN 800-900 in our fleet). We have IAEs of a similar age, they don't have this entry.
Went through the FCOM couldn't find anything. The following is just a guess. In the case of flight on batteries only you will notice that the engine anti-ice valves are automatically open (increased fuel consumption). I wonder if the same thing is done just incase the faulty battery problem develops into something more serious. If further electrical systems were lost, could we guarantee the ability to select engine anti-ice after the event?