Yes, the skin of a marrow is edible. It is stripy, thick, and softens when cooked, so there is no need to peel it unless preferred. The skin can be roasted, fried, or cooked along with the marrow flesh, and it adds fiber and nutrients to the dish. Some recipes even use the skin separately, for example, frying marrow skin is a known dish in some cuisines. Marrow is essentially a mature courgette (zucchini), and like courgettes, its skin is soft enough to eat once cooked. The seeds are also edible and can be roasted and eaten as a snack. In summary, marrow skin can be eaten and is commonly consumed in cooked dishes, sometimes whole with the flesh or separately fried or roasted.
