[SoTrue1920]

If you mean integration in terms of racial parity - there are multicultural sororities (and fraternities) out there already. Many of the professional fraternities and sororities are well integrated. Gamma Sigma Sigma sorority is well integrated, with chapters at predominately white institutions and historically black colleges and universities. Alpha Phi Omega is the same way. But desegregation doesn't technically mean "achieve racial parity" - an organization can consider itself desegregated when one member of a different race becomes a member.

I look at the sororities at UBC near me, and they have Asian, Indian, Black, and Caucasian members -- and the racial parity seems quite good. When I remember my days as an undergraduate, almost all of the NPC sororities had Asian members - therefore, they were desegregated, but not necessarily integrated. Almost all of the IFC fraternities had Asian members; one or two even had African American members, thus, they were desegregated. When I was an undergraduate, we had Caucasian members of Kappa Alpha Psi on my campus. One of the appointed national officers to my brother fraternity (Phi Beta Sigma) is white. I have Asian, Arabic, Caucasian, and multiethnic sorors.

So to answer your question in a roundabout way, the answer is "they already have desegregated, but they're not integrated." As to whether organizations will become fully integrated, I think that largely depends on local attitudes, exposure to different ethnicities, a scaling back on the whole "legacy" system, and -- I hate to bring it up here -- continued support for programs that work to increase and retain racial diversity on college campuses.