You'll only be able to broadcast the authenticator code (one code for all accounts), if you have each account on its own Battle.Net email.

I have five Battle.Net emails, with one wow account on each. And can log in, all five at once, by first broadcasting the password, and then broadcasting the single authenticator code.

I lose the integrated account management features.
And if they ever change BoA items to be across the battlenet (as rumored), I'd lose out on that too.