It depends on how it stayed afloat. At the same time that Justinian was reconquering the west, something very similar was going on in China. The new China obviously never fell, though, while Justinian's descendants lost his hold in western Europe (probably for a lot of complicated reasons, but definitely helped along by humanity's good friend Yersinia pestis). I'm inclined to believe that a unified Roman Empire based out of that could have survived for quite a while, since Byzantium only really fell in the 15th century, although it was getting a little bit crumbly by that point thanks to the Ottomans.
Technology would probably have followed roughly the same course as it has today. Religious and societal trends get a little more complicated. The Protestant Reformation and the philosophical shifts of modern France and Germany had a basis that was fairly complicated and relied on a lot of dominoes falling in just the right way. Not going to get too far into it here (because I can rant about history for hours), but they probably wouldn't have happened. Whether other, similar things would have happened or not is a very, very hypothetical question.