Would be pretty expensive at scale and much has been done to optimize CPU only for search.
Google uses neural nets extensively for search, those run on TPUs and Bing uses fpga for acceleration, presumably also for neural networks.
Both are more efficient than a gpu.
That is for inference. The neural networks are trained using GPUs.
Well yes, but I would assume that this case would be for inference, since GPUs are pretty much train once and deploy everywhere (granted, hyperparameter tuning is still a point).