Yes, schools in Europe have done a bang-up job assimilating Muslims so far...
Check my above reply.
I forgot to answer the question about private schools, of course they do exist, but in many countries students in them do not get their share of tax dollars that would otherwise be used for their education in the government run schools.
Sweden does though have a voucher system, both for private and public schools.
Iceland does require municipialities that allow private schools (I think they have to allow it) to pay for each student in them at least 75% of what they pay for students in their public system.