This could have had some truly facinating social implications. Look at some of their lesser-studied tenets (ever since the publication of the Sana'a papyri we keep learning more and more about their writings).
The point of Islam (I believe it is translated as 'submission' or 'acceptance', but I'm no expert in dead langauges. Not many people read Arabic any more) is that the will of God is revealed as the supreme law. That places it much closer to Judaism than Christianity. I realise some people have referred to Islam as a 'Pseudo-Christian' movement ever since Muhammad was labelled hairesiarch in Antioch, but he is much better as a Neo-Judaistic patriarchal prophet in the mould of Moses. A lawgiver, arbiter and conduit of the divine word, not a spiritual leader of the flock and minister to souls. Now, the really interesting thing is that Islam had no organised rules of successorship to this position. Thus we have an extensive body of law (we have no idea how extensive the 'hadith' really were, but the few pieces we have found indicates that there mucst have been thousands if not tens of thousands of lines, many in high-quality metric prose), but no office allowed to alter or amend it. It is all down to interpretation, and unlike the Christian imperial church, it appears Islam never had any limits on who was permitted to interpret these texts. Just care to imagine what kind of social implications that would have. Widespread literacy, as everyone would be given access to the Law. Dikaiocracy and its democratic structures could have developed early in such a society that needed to establish its religious and political leaders by consensus. The very concept of 'heresy' would be alien to it. I think we have lost much with the withering of Islam. Not that its influence on the mainstream would have been all that great intially - the language barrier between the Arabs and the civilised Aramaic and Greek worlds would have been a great obstacle - but given their embrace of warrior virtues I think the Islamians (is that what you call them? I would hesitate to call them Muhammadans, like we would a Christian heresy) had a political future. The Hejaz is a rich province even today, and they might well have gotten as far as the Sinai and Oman. And offbeat groups can have disproportionate influence. Just look at the Martinians in Aquitaine or the whole breakaway Latin church. They, too, seem to have been closer to Dikaiocracy than we at the time, by the way. The history of the Roman Empire just is a long series of missed opportunities at that time.
Do you think that Islam could have made headway into the East? The Orientals never liked Christianity, its individualistic, non-traditional teachings seem to go against their character. That's why they're pretty much all Shan Buddhists now. But don't you think a more legalistic, organised, less guilt-obsessed faith might have stood a chance? I realise the idea of Central Asian Islamians is odd, but remember, these peoples used to have a warrior tradition every bit as strong as the Arabian one.