The question is valid. But you need to ask the same question for a coal or gas fired plant which does emit GHG over its entire lifetime on top of what was neede

The question is valid. But you need to ask the same question for a coal or gas fired plant which does emit GHG over its entire lifetime on top of what was needed to construct it and what will be needed to deconstruct it. I have heard that there are by now numerous studies that show batteries are better in cars as well as grid. Unfortunately I have no link handy