Given that there could of been no issues for quite a bit of time, since there is a two hundred and more year gap between issues mentioned. The Interregnum didn't occur when Uriel VII and the heirs/Martin all died. Ocato held them together for seven years. So given the two examples, it might depend on the Potentate ruling the Empire until an Emperor is crowned. Before Cyrodiil supposedly erupts into Civil War and split between Colovia and Niben.
So there is the chance Cyrodiil will be fine. Given that they've never actually fallen into complete rebellion right after the loss of an Dynasty, at least to my knowledge. So the Empire could be fine for several years, fall into civil war. Or it could be fine for hundreds of years, before falling into civil war. Or it will be fine, then an new Dynasty is crowned (If Mede line has truly ended). Or it gets destroyed in the Second Great War.