There's nothing you need to do inside of MLS to make this work; the bug will have to be fixed by the development team. Of course, having accurate email addresses in MLS will improve the distribution of any broadcast messages. A clerk can enter those in MLS, or members can update email addresses themselves using the new Directory on lds.org.
I think you have just answered a question I have had on the new email broadcast If I am reading you correctly, anyone with a correct email address in MLS will receive a broadcast, and not just registered members, and any changes or additions to email addresses on the new directory will show on the MLS. If all this is correct, this is a terrific boost to the broadcast system... Now if we can just get the bugs out and get people to list their addresses.