I would say that it was a relatively small degree. Islam taught that all people should accept Islam and that therefore it was important to spread out and expose more people (whether voluntarily or not) to the faith.
It is hard to say, though, that Arabs would not have been motivated to expand had it not been for Islam. It seems that all strong peoples try to expand at some point.
So, I would argue that Islam helped to unify the Arabs and make it possible for them to expand. But it is hard to argue that a unified Arab people would not have wanted to expand if they had not been Muslim.