So which Islam did the Mongols, Manchu, Greeks and Germans (in multiple iterations) use?
It seems to me that tribes/cultures on borders of empires have a pretty recurring tendency to unite, even if that unity is fragile. Islam helped stabilize the Arab conquest so that they didn't fall apart into Arabia+Mesopotamia, Persia, Egypt, and whoever else immediately after the conquests stopped, but that's not the same as being needed for conquest in the first place.
Arabia had been on the borders of various empires for millennia (literally the first empire in history was Sargon of Akkad's in Mesopotamia) without ever showing any real signs of uniting to go on a conquering spree. That they only did this after converting to Islam suggests that Islam was indeed an important factor.