It could be. When my gliders had a respiratory infection, the vet said that the cold air from open windows could have been a cause. That and stress because I had just moved them across state. Maybe he was stressed out about the new cage cover. I don't know.
Just keep them warm enough and don't let any drafts near them. Limit stress. That's the advice that I got from my vet.
Maybe this is a more...strange explanation but is it possible that he could be allergic to the new cover? Not sure why that would make him sneeze only when he ate but it's a thought. A wonderful book I read recently was Eliminate Your Pet's Allergies
by Devi Nambudripad. Pets have so many allergies that do not make themselves known in the traditional ways.
Let me know what the vet says!