From a literature search, yes, you are correct, Bradford pear pollen is not allergenic because the pollen is spread by insects, not air. The flowering tree can cause an irritant effect by its unpleasant smell.
Bradford pear (Pyrus calleryana) is not listed as an allergen in an extensive review (Kosisky SE, Marks MS, et al: Pollen aeroallergens in the Washington, DC metropolitan area: a 10-year volumetric survey 1998-2007. Ann Allergy Asthma Immunol 2010;104:233-235.)
Patricia McNally, MD, FAAAAI