Absolutely not. The Xbox 360 power supply is electrically and physically incompatible with the original Xbox. Using it will permanently damage the original console.
| Specification | Original Xbox | Xbox 360 |
|---|---|---|
| Connector | Round 4-pin (proprietary) | Rectangular keyed (proprietary) |
| Output Voltage | ~12V / 5V / 3.3V (multi-rail) | 12V / 5VSB (varies by revision) |
| Max Wattage | ~150–180W | 203W / 175W / 150W / 135W (rev dependent) |
| Pinout | Unique | Unique |
You cannot physically connect them without cutting/splicing wires. If you did, the wrong voltages on the wrong pins would fry the motherboard, GPU, CPU, and drive electronics instantly.
Never mix power supplies across console generations. Buy the correct unit for your specific console model.