To address this another was...that Christianity is a powerful thing and has given its adherents an advantage in terms of social cohesion and conquering force is true.
And that potential, to replace the flagging effectiveness of the existing Roman religio, is probably an important part of what Constantine saw in it when he took a minor but vibrant cult and fused it to a titan. The Eastern Empire went on for a thousand years with the church as its rallying point, after all, and it was pretty damned effective, although it wasn't enough to stop the eventual decline, and by the fifteenth century Constantinople was only a symbol of a vanished greatness, and then the Ottomans took it. But only a few centuries later new and even more powerful Christian empires were rising.
Despite the popular myth, Christianity did not actually keep Western Europe down. The cathedral towns were the last bastions of civilization over much of Europe, in the wake of the fall of the Western part of the Empire. (Which wasn't because of Christianity either; the conversion was an attempt to slow a decline already well begun, and the East made it work.) The Church was all the literacy and learning Europe had in the Dark Ages, and while abbots may have bemoaned the way their monks sang popular songs and recorded things like Beowulf and were altogether less than saintly, without the monasteries our record of history would be much the poorer, and Europe would probably never have roused itself from barbarism. Christianity honestly was the backbone of Western learning, and its link to the classical era. This is the historical reality, as someone whose specialty the subject was at university.
History shows there are in fact advantages to using Christianity to tie an empire together. It also shows that Islam works at least as well, but only if your people are or are willing to become Muslims. State Shintoism was formed in the twentieth century to imitate the unifying powers of Christianity, and did okay. The Romans had free and cheerfully syncretic religion as long as you joined in the major public rites, too, and they gave special exemptions to people like the Jews, and that seems to have worked okay. Well, except the Jews; letting them stay out of the state religion provided a stronger emotional basis for their sense of alienation from the empire, so they rebelled and got their Temple demolished and stuff. They had a very strong ethno-national consciousness all along, so the uprising was probably inevitable anyway. But generally it worked for quite a long time.
So...basically, religious inspiration helps empires, and the only practically feasible one to use in America would be Christianity, if we were so inclined. Just because of demographics and the historical context. And thus you would like us to use it that way, I guess?
But that's kind of a disgusting lack of integrity about religion from anyone who isn't Emperor of Rome. And I'm pretty sure it wouldn't fly in the modern era. Modern communications and ideologies and the literacy rate all make it much harder to unite people sufficiently around something without constantly oppressing them into it. See: Communist bloc.