You can certainly do your EU EASA certification before coming to the US, and the FAA will grant privileges based on your EU licensing. You'll find it a lot less expensive to get your certification in the US, however, than to do it in Europe. That said, if you plan to go back to Europe and fly there, it will be more expensive in the long run to go to Europe and get EASA certification, unless you do it in the US at a place that can handle both. There are several locations that do.