It would really depend upon the tribes' relationship with the Church after their conquest. If they give the church autonomy and don't try to oppress the Christians, I could certain see the Roman population going along with it for the time being. In some ways, relations might even be better; dealing with heathens is often easier for people than dealing with heretics (those who SHOULD belong to our group, but don't! And that's offensive and dangerous!) If they, on the other hand, attempt to crush Christianity, then they would have the mother of all invasions/rebellions going on.
Now, the problem of course, is that Christianity is the region's prestige faith and the 'door' into Greco-Roman culture and civility and the Germanic leadership are going to want everything that comes with it to legitimize their own rule. So I suspect you would still see the leadership convert to Christianity in fairly short order. Furthermore, especially for groups like the Ostrogoths, it will be even more important because being Pagan is just asking for the Eastern Emperor to suddenly decide he hears the groans and cries of the oppressed Christians of the West.