I doubt Google would design its own ARM core -- I think Cortex A9 multicore would be fine for its purpose. But they may design their own chip built around this core. Server chips won't need the graphics and signal processors that most high-performance ARM chips have (as the latter are targeted at media applications), but may need larger caches and MMUs capable of addressing more than 4GB of physical memory. Even if ARM has only 4GB logical address space, you can let different processes have different 4GB chunks of a larger physical memory.
But, instead of designing their own, Google may just ask Marvell, Qualcom, Nvidia or TI to design a chip to their specifications. If Google promises to buy a million chips per year, I'm sure these companies would be quite happy to do so.