I have to say it is astonishing how much the inhabitants of Brython believe the history of the world revolves around their isle. In short - no. The end of the Roman Respublic would be entirely unaffected by the non-events in some outpost. A failed revolt just means the Roman troops retreat after the end of the Julio-Claudian dynasty to be used in internal conflicts. There was very little of value in the isles, and they were invaded at all only for reasons of prestige, at the brief height of Roman power.
The matter of Jesus is completely unrelated, of course. Christianity didn't properly reach much of Western Europe until the end of the Han era, long after the collapse of direct Roman rule. It was unsuccessfgul in Brython largely due to the fact that the priestly collegia there held a greater degree of power than in formerly Roman lands. And rest assured, speak a Romance language we may, but far from all of us are either Jesus-worshippers or decadent. Roman civilisation at its height was equal to that of Da Tang, with great cities and minted currency. Brython's unique economic posdition is largely due to it having been the point of first contact, but we know now that contact was long established overland. Missionaries even brought knowledge of the Path here when Rome still ruled.
(OOIC: obviously a ridiculously huge butterfly effect in play here)