Would it be anachronistic to use modern concepts and apply them to ancient empires?
How are you defining "statehood" here? It is a pretty slippery concept, often in ancient studies it tends to just be used to categorize polities that pass a certain level of socio-political complexity.
There was certainly a concept of the state - the civitas - in which citizenship denoted shared membership of a community defined by its relation to a body of governing institutions in a defined polity: to that extent statehood is there, though it had existed in Greece too. But as citizenship reflected social status rather than just birth within a territory, it still falls short of modern concepts of universal membership of a community subject to a common authority. The same could be said of medieval societies too. To use the term "state" for the government and its agencies would not be anachronistic: there was a concept of statehood, but it differed from our modern one.