It will be interesting to see how such a secular country handles this issue.
Though, I have to say this:
Most of the Islamic immigrants to the US had a level of influence in their former country. Most of the Islamic immigrants to Europe are from lower castes in war-torn countries and bringing their wars with them. Minnesota is having the same problem with the influx of Somalians.
In other secular European countries things seem to be going from bad to worse concerning their immigration policies, particularly from moslem dominant countries.
Various measures have been taken, in Switzerland they have banned any more minarets being built, in Denmark they have banned any more mosques, at least in Copenhagen.
France seems to be losing territory to islamic dominated areas where moslems actually rule and even the French police don't venture.
Britian seems to be taking appeasement to insane lengths.
The Netherlands, Belgium and Germany are facing the same sorts of problems.
While what you say is true of Amerca vs Europe, still we have been admitting around 100,000 moslem immigrants for the past forty years, not counting illegals and we really have no idea how many children have been born to those moslem immigrants, so if you look at the history of other nations who have had vastly growing numbers of moslem citizens you invaribly see a pattern of increasing islamization of the host country.
Increasing diversity (on many dimensions) puts a strain on these social contract countries. That and increasing population.
A country like Norway has a small, relatively homogenous population and the country has massive oil revenues. It's all fine and dandy until you have large scale immigration with people of different values, cultures, work ethics, etc.
Norway has also had it's share of problems with moslem immigrants, even if Norway can afford to foot the bill for it's welfare state, you still see cultural pressure such as rape by young moslem gangs who are promoting the values of the country from which they migrated.