If Napoleon conquered Italy, Italy was assimilated into France for around 500 years, to the point where it was culturally French and the people considered themselves Frenchmen...and then France fell, then yes, it would certainly be just as French as France.
The thing about these comparisons is they ignore that Rome had control of the east from circa 60 BC (and as early as 133 BCE, as far as Asia Minor was concerned), and that control persisted for over 500 years before the west fell. During that time, everyone in the empire was granted Roman citizenship, the citizens in the east undoubtedly referred to them as Romans, and the senior emperor mostly ruled from Constantinople or Nikomedia for 200 odd years. Not to mention, the capital in the west hadn't been Rome for around 200 years either.
Nor, was Italy the center that everything revolved around since the second century. Rome had emperors from Spain, Illyria, Thrace, and North Africa, almost all of Rome's soldiers were non-Italians, and the most economically vital regions of the empire were Spain, North Africa, Egypt, and Syria. Hell, a sizable proportion, if not an outright majority, of the Senate wasn't even Italian.