PC/WI: Restoration of the Roman Republic during the Third Century Crisis?

So, assume that the Roman "barracks emperors" are even less competent at defending the empire from the Germanics, Persians, and other usurpers, and the whole thing collapses into multiple squabbling states sometime around the 270's AD.
One of the Germanic tribes, led by their king, estabilishes dominance over Italy, encircles the city of Rome, makes alliances with the local aristocracy, and fights against an imperial successor state in North Africa.
One idea i had whose plausibility i'd like to verify would be the old Roman Senate, still present in the city, becoming disenchanted with the whole imperial experience, abolishing the office of the Emperor and restoring the Republic. Could the king of the Germanic tribe in Italy end up supporting the Senate, promising to keep Italy safe while ordering the restored Republic to maintain its borders at only Rome and its neighbourhood, forming the basis of a new city-state?
 
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