Well, Roman polytheism, isn't a religion in the modern Western sense, so it really couldn't take the place of Christianity in any meaningful way. I suspwect, though, that a lot of the cultural developments that happened IOTL with Christianity would still happen ITTL. Religion as a motivating factor for everyday behaviour is overrated. Those Roman polytheists would very likely still experience a contraction of political space, a quasi-Platonist reverence for the otherworldly and disdain for the physical, a culture of scriptural learning and a decline of urban society. These things were part and parcel of therir history and culture, not outcomes of their conversion.
Northwestern Europe would most likely suffer most from this, because Catholic Christianity created a conduit of Mediterranean cultural values and social technology without which they may be left to try out nonviable approaches for longer. But even that is not a given, looking at the way Viking society developed functioning large polities without depending on a literate clerical class.