Is treatment for allergic rhinitis going to be effective if the patient is stil exposed to the allergen?

Yes but: If you are talking about medications, they will remain effective but the symptom control will likely be reduced if you are exposed to a highly allergenic allergen. Thus it is not an issue as to whether the drug is effective, but whether the allergen exposure is overwhelming. Allergy shots however often allow people who are allergic to pets to be able to live with the pets they cannot part with.