The problem I have with this is: it's so obvious and straightforward that, if it is was that simple, other scholars & academics (who don't have a magical dog in this fight) would just say that's the truth and put it to rest. But they don't. It doesn't appear to be that definitively, obviously meaningful in this way. And since, to the Romans, it would've been more apparent that it sounded like ad (in its native culture & language), you could expect they would dismiss it. But the square's been found at Pompeii, among other places. Neither the contemporary Romans, nor scholars today, seem to be responding to it as you do in your interpretation.
Is your interpretation possible? Yes; along with the other possibilities given in this article. Possibly also, it's wrong. In that situation there's no particular reason to privilege it above the other possibilities. It's a big question mark - but even things with mysterious origins (say, the Tarot - a "mere" game) have proven to have some real mojo.