I have 2 experiences with this - one was my own son who also turned out to have adenoid issues and when he was 2 had them removed and then he was fine and at 17 he never gets sick - not a sick day from school ever!
Now in daycare I had a girl who was constantly snotty - really gross - they finally figured out it was an allergy and started her on some puffer - they tried to not use them because they don't approve of them - but found that when they did she was so much better that they are actually using the puffer. Again - several Dr. visits and me mentioning every day that she was really clogged and could barely breathe.