At the very least, half of the cache is disabled. They cherry-picked a feature from the Pentium III lineup that they wanted to keep while lowering the cache to Celeron levels. It's a deliberate modification to reduce cost while maintaining desired performance.
It's not detectably customized beyond that but it's not like it's a SKU you can buy off the shelf, either.
I didn't?
> The Xbox had a customized Coppermine Pentium-III era processor from Intel.
The original xbox was a PC in a box, the CPU was not a customised part.