The short answer is, YES. Although much more common triggers are food-allergens.
Doctors have learned that even complete food elimination diets (elemental diets – liquid nutrients only) sometimes do not resolve high eosinophils counts. In these cases they believe they likely are environmental allergens (or aeroallergens) causing them. These allergens are breathed in, or even exposed to the esophagus when swallowing nasal mucus which can be concentrated with environmental allergens breathed in through the nose and they coat the esophagus when swallowed.
There is also a “both-scenarios” diagnosis by doctors. Many doctors have noted a correlation to worsening eosinophil counts (and worsening symptoms) during the high-allergy times of seasons. That doesn’t mean the environmental allergens are “causing” the higher eosinophil activity, BUT they may result in a worse food-allergen reaction because of the environmental allergens. The true correlation is still not completely understood, but it has been documented that allergy season will sometimes make food-allergen EoE worse.
For those who find no relief with food elimination, the second level of defense is looking at aeroallergens. See this article for a full description of study results.