HyperSizer does have beam-column capability to account for initial imperfections or applied pressure superimposed with compression loads. The details of this can be found by going to HyperFinder (under the Help menu, go to technical document search) and then search for the keyword "beam-column".
We do not yet have this effect for sandwich ramp-ups. I believe the beam-column effect for a ramp-up would be caused by the induced bending moment you get at the ramp-up from eccentricity between the edge band and the sandwich itself.
We have done some work recently on trying to include ramp-ups including the effect that the ramp-up has on the out-of-plane shear force (Qx), however that effect is not yet in the software. When we include the ramp-ups, I believe that the beam-column effect you describe would be included.