The gagging when waking up and the snoring may or may not be related. If there is some inflammation of the sinus (sinusitis) then sometimes the drainage can drip down the pack of the throat and lead to some gagging when waking up. Otherwise there may be a secondary gastrointestinal inflammation as you had thought.
Causes of sinusitis may include: (as Jim Hall pointed out) upper respiratory infection, allergies, dust, primary sinus infection, and less commonly polyps, fungal infections, masses, etc...
If your veterinarian is not concerned about infection and is just siting 'congestion' then she or he may be thinking of dust or allergies. An Hepa air filter may be beneficial as well as either a humidifier or keeping the cat in the bathroom while you shower. Humidity can help clear the sinus cavity.
If these are not working, then perhaps talking to your veterinarian more may help. Your vet may want to try a course of antihistamines if allergies is still of a concern.
Hope that helps.