Yes, luffa gourds are edible when harvested young.
Early green luffa gourds are a great summer fruit. It can be harvested and eaten similarly to zucchini or squash. Luffa gourd has a small window for use as fruit. As it matures, its center becomes fibrous and not suited for eating. Its mild and sweet flavor makes luffa gourd great sliced, grilled, and sauteed, or in soup, curry and salads.