Except of course that Egypt has 80 million inhabitants and is by far the largest Arab country; a Syrian scenario is not an option. Not that that's likely, fortunately. I don't think you're right about Lebanon - things are tense, but the Lebanese know what civil war looks like, and they're not stupid. Iraq looks worse, but there too people know quite well where things will end if they let it slide too far.
3 centuries ago, is it? Let's not overestimate the extent to which European countries or the US are secular in their politics - France is, I suppose, but France is hardly much of a shining example. I don't think I even need to mention the American religious right, or the influence that Christianity had and still has on the conservative parties of Spain and Germany, to name only two obvious examples. Go back a little in time - less than a century, never mind three - and you get to things like the Belgian Socialists and Liberals (I'm not sure about other countries) postponing voting rights for women for years if not decades on account of "they'd just vote for whoever the priests told them to vote for". In Europe that age is ending, yes, though probably not as fast as some would like to think, but in the US it doesn't really look that way. How often does an openly atheist politician get elected to national office?
The Arab countries will have to get a working democracy going in much less time than the Western countries did, and it won't be easy. But a lot of people in the West need to get over their delusion that "democracy" means that suddenly the Arabs will see everything precisely like us and forget about their religion and culture. And they also need to realize that the Egyptian secular establishment may seem nicer and less alien to the West than the religious middle class does, but then that's because the secular establishment and the armed forces in particular can only maintain their plutocracy with Western support; which doesn't precisely endear the West to said religious middle class.
And really, when you get down to it, those Muslim Brotherhood voters are not that "alien" that a Westerner can't understand their frustration and anger, if he's merely willing to engage in a few thought experiments and put himself in their position for a moment.
I hope you don't actually believe that final prediction of yours, in any case I for one think it's rather, well, apocalyptic as I said.