First of all, the premise is extremely unlikely. Germania would be extremely difficult to conquer or maintain, and such a money sink would probably accelerate the collapse of Rome. Also, while the reign of Augustus is the one of most likely points for any process of conquering Germania to begin, it would almost certainly not be finished during his reign. Conquering all of that land would be a monumental task, and if Augustus had any sense (which he did), he would likely conquer a small part of it and leave the rest to future emperors. Slow and steady wins the race, as they say.
That said, barbarians could still invade and deal a heavy blow to Rome, if not destroy it as in real life. The Huns would probably be the first such group, and might be able to sway some tribes to their allegiance, unless they were very heavily Romanized. If Rome somehow maintains control over the Germanic tribes, then the Huns could probably do some big damage, but not destroy it.
If the Huns failed to destroy Rome, then Rome would probably collapse in the face of the mass migrations of Turkic peoples, Slavs, and Magyar. I just don't see Rome as being able to maintain an empire all the way to the Vistula (the historical boundary of Germania) in the face of such a large influx of nomads.