Conquering is going to be hard to pull off, for the reasons listed above, but if you want to get a Siege Mentality/protective militancy in place I think you could easily pull that off if the Germanic invaders had been Pagan rather than Aryan. As the Emperor's direct control of his Legion's slip and there's a need to try to secure outer regions by a force that isent going to leave its post to appoint its general Emperor, I could see Rome tasking the Church with raising "Mighty Fortresses for our God", setting aside land to be managed to supply early Templar forces set to defend the region, it's faithful, and the civic and ellessiastic records. As the Empire breaks down, this network of militas remain and develop a loose informal hierarchy in the West, acting as strong points of the Faith against the Wodinists until centuries of effort convert them (at least in the Med. Core and France). Of course, by then you have the Arabs starting to knock at the door...
In the east, this would certainly make the schisms more... interesting. The Church would be far more of an independent political force from the ERE if it has its own armed wings, fortresses (Which could have easily developed into citites) and major revenue streams. Or maybe theyre integrated into the Imperial military structure out there. Of course, in either case it would also run into more problems being allowed to continue operating if their areas are conquered...