You'll suffer. Obviously you'll continue to have nasal and eye symptoms. Also, a certain number of individuals will go on to develop asthma or if they already have asthma it will get worse. It has been well documented that controlling nasal symptoms decreases asthma symptoms. Current intranasal corticosteroid sprays and 2nd generation non-sedating antihistames are very effective with few, if any, side-effects.
See below. The symptoms, either runny nose, sneezing, cough, or a rash, would not get any better, until the exposure is gone.
What would happen if year round grass allergy is not treated, and you get nose symptoms all the time?
Symptoms continue. Usually grass allergy is seasonal. Year-round symptoms usually suggest environmental allergy as well. You should be evaluated for that possibility.