AHC/WI: Germanic Invaders of Rome Get a Mohammad

In Late Antiquity, many of the Germanic tribes who would go to invade the dying Western Roman Empire (Gotha, Vandals, etc) converted to Arian Christianity, an interpretation of the faith deeply at odds with the Chalcedonian Christianity of Rome and Constantinople. Though Germanic invaders did carve out several kingdoms in the Western Mediterranean, they did not radically change the culture of that area - the Arian Germanic elites didn't really attempt to convert the locals, and ultimately many assimilated into the majority culture of the areas that they conquered, adopting Romance languages and Chalcedonian Christianity.

My question is, how possible is it to give these early Germanic invaders a Muhammad figure? This wouldn't be an exact parallel to OTL Muhammad, but I'm talking about...

1) Someone who can use Arianism as a basis to unite many or most of these Germanic tribes into a single cohesive religious/political/military force.

2) Said force successfully conquering most or all of the Western Roman Empire and Western Europe, and perhaps even further, in the same way that the early Muslim invaders conquered most/all of the Byzantine and Sassanid empires, and further.

3) When and if this empire falls, that it can firmly implant Arian Christianity and Germanic languages in at least Southwestern European and North Africa in a way that the OTL German peoples were not able to do.

How early would the POD have to be?