I say that it sort of did, and sort of didn't. Without going into a long essay, I'd say that it clearly had a "Christian" tone to it, but was not really something I'd feel comfortable calling a "Christian society".
Some of the states, for example, mentioned scripture verses right in the laws they passed (and I think even the constitutions they wrote). "God" is talked about often, and while many founding fathers did not want an establishment of an official state religion, certainly some religions were more favored among the general populace, and some were very much less favored (to the point of persecution).
On the other hand, most of the Fathers seem to me to have been Deists and/or rationalists. I believe it was Thomas Jefferson who cut out the miracles from the Bible, and there are other such examples of activity that we would hardly identify as Christian. They clearly saw the Bible as a foundational text, but so do many cults, but that doesn't mean that the cult's experiment works. The founding fathers did, after all, call our country (or government) an experiment.