My gars don't go after plant matter, per se. However, they need the nutrients, vitamins, amino acids, etc. derived from plant matter. In the wild, they normally receive these through devouring herbivorous/omnivorous prey species.
But, if your gar likes zucchini and other veggies, let him enjoy them. They'll only benefit him and his health.
Mine do snap up veggie sticks. But, I figure it's because they resemble the earthworm and aro sticks I also feed the tanks.