Yes, with the Diffusion method you can also spectrally sensitize a unsensitized AgX emulsion subsequently. In contrast to former bathing methods, this one uses a halide/dye/ascorbate solution for sensitization. I think it's this combination that does the spectral sensitization more efficiently than previous attempts.
As for forming larger grains with the Diffusion method, you could well do that by adapting the bath concentration. E.g. increasing the amount of halide most certainly does increase grain size. Similarly, longer bathing periods in the halide bath will equally favor the production of larger grains. Furthermore, you might increase the temperature of these baths and the drying section etc.