Honestly, I don't know enough about this to answer definitively. I wrote that after reading through the AISC commentary on J10.4. That states that the sidesway web buckling provision were developed to explain away some failure that occured in test specimens which had their compression flanges restrained.
But, re-reading the section I think you're correct. The issue could probably happen at any time. For a wide flange beam with an un-restrained compression flange, I would then this failure state would never control (because the compression flange buckling should control).
Your case is interesting in that the compression flange is not restrained. But, it is reinforced. Therefore, I would think it would be possible for sidesway web buckling to still occur. In fact, since the neutral axis of the beam shifts up (and a larger portion of the web is in compression) it might even be more likely to occur for your case.