Does Xcode use GPU to build?

No reason for it to need the GPU when building - why do you ask?

Xcode is not itself a compiler, it just hosts the compiler. For Obj-C, the current (preferred) compiler is clang. You can visit clang.llvm.org and if your question isn't answered by the information on the site, there are mailing lists where you can ask about implementation details and strategy.

My guess, though, is that the compiler isn't designed to use the GPU.

>> No reason for it to need the GPU when building

No particular reason, but it's certainly possible that it might use something like OpenCL to offload some processing onto the GPU.