Yes. Minecraft: Xbox 360 Edition (Legacy Console Edition, TU73 final) includes the **Hunger Bar** (added in TU8 / Beta 1.8 equivalent).
Xbox 360 Edition lacks Hunger Overhaul-style configs, but core mechanics match Java Beta 1.8 – Release 1.12 (pre-Update Aquatic).
Keep a stack of cooked steak; you'll be fine.