Hard to resist Tom's invocation...
This approach has been tried before. So has the reverse arrangement: Using a material designed for HIC in the reversed-phase mode [ref: R.H. Ingraham et al., J. Chromatogr. 327 (1985) 77-92]. The arrangement you propose doesn't work well. The reason is that C-4 coatings have alkyl- groups packed closely together. As Tom points out, coatings designed for HIC generally feature moderately hydrophobic ligands (phenyl-; propyl-) attached to a reasonably hydrophilic backbone polymer and the unit cells tend to be large, resulting in a low density of the hydrophobic ligand on the surface. This arrangement works well for intact proteins, which is the application that one normally uses HIC for. The conditions tend to preserve protein tertiary structure (unless it's a subunit protein in which the subunits are associated through electrostatic attraction, which is disrupted by the high salt concentrations). The intact proteins cover so much area on the surface that there are enough hydrophobic ligands available for adequate retention even if they're sparsely distributed; it doesn't make a lot of difference if the protein is sitting on top of 4 such ligands or 14. By contrast, small solutes with hydrophobic character can line up with the ligands one on one, and ligand density makes a big difference. While it's possible to separate small peptides via HIC (A.J. Alpert, J. Chromatogr. 444 (1988) 269-274), peaks are wider and backpressure's higher than with reversed-phase.
Getting back to your question: It would be appreciably more difficult to get an intact protein to elute from a C-4 material. The necessary conditions might cause the loss of its tertiary structure. That in turn would expose all the hydrophobic residues that are sequestered in the core of the normal structure. They could bind to the surface in numerous alternative orientations, each with a different degree of affinity and eluting at different points in the gradient. Result: a peak 15 minutes wide. There are reasons why it's been necessary to develop alternatives to reversed-phase for protein chromatography.
