Kind of. The empire was multi ethnic and so are modern Americans however often the question is about the foundation. Who are the descendants of the foundational Romans. Did they get diluted into oblivion? For Americans it’s easier as we can trace descendants of the founders of the nation. Of course Britain itself is the result of many waves of immigration, the neolithic, the celts, picts, romans, jutes, angles, saxons, norsemen, etc.