It depends on what your definition of diversity involves.
If it is simple RACIAL or SEXUAL diversity, then it's not so. The diversity that is so good is the INTELLECTUAL diversity from each unique individual. That MAY come from different cultures, but those cultures shouldn't be racially or religously specific. That really doesn't matter.
We CAN have tremendous DIVERSITY from other European cultures. It DOESN'T have to come from a different group based on race, ethnicity, gender or religion. It MIGHT, but it doesn't guarantee any more diversity than anything else.
Diversity based on p.c. (race, ethnicity, gender. sexual orientation or religion) is crap, racist, bigoted, elitist, sexist, relative-morality crap.
Here is a nice definition of diversity spouted by a black St. Louis alderwomwn to her white colleagues: "Diversity doesn't mean I have to listen to you, it means you have to listen to me." This is diversity I could certainly live without.