I said I would come back with the answer, so here it is!
According to the Medical Department at Gatwick, the answer certainly isn't a straight "no". It depends on the severity of the current condition and reassessment by an independent immunologist would probably be needed. If a medical certificate were to be awarded it would probably be with Operational Multicrew Limitation. I'm not at all sure what implications this might have for prospects in training, sponsorship or employment, though. For the time being we are returning to the immunologist for retesting and an up-to-date report of the condition, as the last time my son was tested was about five years ago.
The Sheep Pilot might also be interested in this!