Integration will only push over businesses as non constituent organization records through Integration. The business information will come over as long as the organizations are linked in the linking grid.
If the organization relationships do need to become full constituent records, we could manually convert the relationships to constituents in the Raiser's Edge. We could also export the businesses from the Education Edge, import them as brand new organization records in the Raiser's Edge, and the records will show up as full constituents in the linking grid to link. This process would need to take place prior to pushing the non constituent business relationships over to Raiser's Edge.