No, or at least not that we can tell of. The transition between a republic and a monarchy was only in the government of the city of Rome, other cities had their own civic governments that were unaffected. Now, the government of the city of Rome also had control over the empire, but the Roman empire was not organized as a federal system with power devolved from the top. Rather, it was a collection of preexisting cities that were still largely autonomous outside of a few areas like taxation and the military.