First of all, the word “symbol logic” is pretty vague.
But, either way, with the most rigor possible, AE would still be “verbal” in the sense that everything meaningful would be an arrangement of words or symbols referring to something. Sure, we could build a “symbolic logic” to express it with; however we wouldn’t get anywhere without substituting a bunch of meaningful symbols into it in the right order and whatever. In fact, it would be possible (for all I know) to build a symbolic logic which would mechanically rid of us any errors in deduction; but it would still be possible to express absurdities with it: After all, plenty of our imaginary constructions are totally logical; the only difference between them and our models of the real world are whether the assumptions apply to reality, and of course that’s a matter of empirical evidence, not of deductive logic. Sure, AE requires doing a lot of deductive logic/reasoning (mostly because we express it with a natural language, and for some reason tolerate having 1,000 synonyms); but it’s still grounded in realistic axioms - which aren’t always totally obvious.
But, with that said, it’s important to understand that AE is in its infancy, and simply wouldn’t be able to handle the rigor that imposing a constructed language (like a symbolic logic) onto it would suggest to us. (Right now, it’s more suitable to being expressed with the dust and ambiguity of a natural language.) For example, read a bit of Human Action, and just ask yourself whether we could make all of the inferences and axioms totally explicit at this point. It’s absolutely staggering just how many implicit assumptions that he simply takes for granted. At every turn, we find a practically countless number of them. Sure, it’s as rigorous as real economics gets at this point in history (at least as far as I know); but that’s not to say that it’s even close to warranting trying to spell out all of the inferences (especially since most of the inferences revolve around trying to wade through the useless intricacy of a natural language). Indeed, it’s hard enough just to follow what’s explicit; so try looking under the surface, and you will find yourself absolutely bewildered. But that’s not to say that it isn’t possible; it’s just to say that, if somebody pulls it off, it would be a momentous innovation, rather than a mere translation.