If there was still the catchment area ruling with schools then 350 houses being built would be a serious issue .But because you can virtually send you kids anywhere these days, anyone moving into this area would probably keep there kids at there previous school, if logistics and circumstances allow.
My wife used to be a receptionist at a local doctors and knows at first hand that people can’t be bothered to change doctors when they move .
As to whether Llay would cope with 350 houses ,it probably would ,just take a look at the village of Farndon , that at the moment is expanding rather quickly with more houses in the pipeline !