I think this is correct. If Islam is strictly a religion, then banning it would be tantamount to wiping our arses with the Constitution. However, these theocrats will do the wiping for us if we allow it.
The cartoon controversy shows that much (maybe most) of the islamic world simply will not be content to co-exist with the west. They are always going to be trying to overwhelm the west, and as long as they are allowed to freely immigrate, they will not be stopped.
The article of this thread tries to analogize Islam to the KKK, but I don't think that's a good analogy: the KKK may have claimed to be religious, but they didn't claim to be a religion rather each KKK member was a member of another religion and they all shared a Christian (used loosely) belief.
I think your analysis is closer to the truth: Islam is as much a form of government as it is a religion. The first amendment would not protect the governmental part (just as you see Ontario prohibiting sharia while permitting Islam).
Assume some religion that had a practice of sacrificing virgins but was otherwise law-abiding; under the first amendment, they would be free to continue, as long as they gave up the illegal part.
We might be able to outlaw the non-religious parts of Islam (e.g., sharia, jihad, murderous fatwas, and the like), while observing the first amendment protection for the religious part. Those Muslims who could not abide by such restrictions would be free to leave, just as the virgin sacrificers could leave if they didn't like having to live by our laws.
The fact that Islam is as much a philosophy of governance as a religion is a crucial point that most of us in the West do not understand. Islam focuses as much on the temporal as on the spiritual and can not be viewed as only a belief system comparable to Christianity since the Reformation or to Judaism...the aggressive aspect of Islam will render it incompatible with the beliefs of others until it undergoes its own reformation.