No. Original Xbox games (2001–2005) are not compatible with Xbox 360.
Hardware Barrier
Original Xbox: Intel x86 (Pentium III) + NVIDIA NV2A GPU.
Xbox 360: IBM PowerPC Tri-Core + ATI Xenos GPU.
Instruction sets, graphics APIs, and kernel are fundamentally different. No emulator was ever shipped.
What Does Work
Xbox 360 games on Xbox One / Series X|S: Hundreds backward compatible (often enhanced: 4K, FPS Boost, Auto HDR, Quick Resume).
Original Xbox games on Xbox One / Series X|S: ~40 titles backward compatible (e.g., Halo: CE, Halo 2, Fable, KOTOR, Jade Empire, Ninja Gaiden Black). Insert disc → download enhanced port.
PC: Many original Xbox games have PC ports (GOG, Steam) or run via Xemu/CXBX-Reloaded emulation.
If you have original Xbox discs, you need an original Xbox (or modded/emulation) to play them.