Among the many misconceptions about CI, such as some mission against the Classics, “not teaching grammar while providing CI” is probably the most-cited, yet misinterpretissimus of misconceptions.
We teach grammar, oooooooh do we, although mostly in the context of complete Latin messages since even words/phrases contain grammatical information. There’s even explicit instruction, too, though brief student-initiated pop-up grammar explanations (e.g. “Mr. P, why does that word end with nt and not t?”) comprise most of this in a comprehension-based communicative classroom.
Still, even after all that, we do give explicit instruction when students are ready, usually in years 3 or 4. That’s right—even CI-advocating teachers explicitly teach grammar, and they do so using a host of methods and method-free strategies—all grammar-translation alternatives.