No. Islam is not a relationship with Allah. It is a set of beliefs and practices. There are many who consider themselves Christians based on beliefs and practices. I submit that these clearly religious activities do not insure a relationship with the living Christ.
Islam is the Arabic world for "submission". A person who follows Islam is called a Muslim, which means "one who surrenders to God."
That's a Muslim's relationship to Allah. If it walks like a duck and talks like a duck...