With respect to the fact that the "counter-thesis" has been defended by some good historians over many years, I think we can say with some confidence that the counter-thesis is not correct. Roman civilization in Britain, for example, was destroyed by pagan Angles, Saxons, Jutes and Danes. By the time of Charlemagne, they had been re-Christianized chiefly by Gaelic monks who came from Ireland to what is now Scotland, and from Scotland south into the Germanic lands.
These Gaelic monks were never part of Roman civilization: although the Romans appeared poised to invade Ireland from Chester, where they built a fortress for a legion ("Deva Victrix"), they did not follow through; and of course what is now Scotland was at the time mostly held by another civilization, the now-extinct Picts, who were beyond Hadrian's wall. The Gaels (called "Scotti" by the Romans) had only begun to establish some footholds in what is now Scotland; even Dal Riada was not established until after 500 AD.
The collapse of Roman civilization in Britain happened before Mohammed was born; by the time he was alive, in fact, it was all over.
Islam may have been responsible for a similar destruction in Spain especially. If the Saxons did it elsewhere, though, there should be a unifying cause that permitted both effects. That will be found (I think) in the period of the barracks emperors; the consequent gutting of the native Roman military, and the civic culture that had produced it; and the rise of Germanic mercenary forces to supplant native-Roman ones, out of which grew Charlemagne's war band (and the Anglo-Saxon ruling system as well).
To put this in Aristotelian terms, Islam can only claim to be the efficient cause of the destruction of part of the Western Roman world. The formal cause was the internal dissolution, which is universal to the areas affected by the various invasions.
The final cause? If we still believe in final causes in history, it would have to be something like the divine plan: a will that there should be a Charlemagne, or a King Arthur. Most Western thinkers today, however, don't believe in final causes in history anymore: the idea has been discredited by Marxism (which argued for the inevitable collapse of capitalism from something like a 'final cause in the arc of history').