Yes, but it depends what purification technologies the purifier prefers.
First, if the pet in question is a cat, the problem of pet hair needs to be looked at together with dander, feces and urine. No one is allergic to pet hair/fur. It is the dander (tiny dried skin flakes), feces and urine that produces cat allergies in some people, according to petmd.com. These three things, however, can be on pet fur.
An air purifier that contains a filter pad captures dander and floating hair dust particles. One that contains zeolite will capture the ammonia in urine. While activated carbon will capture fecal odor. One that contains all three -- along with a powerful fan -- such as the Purrified Air pet air filter -- is particularly designed to combat the problem.
Even the right air purifier cannot do the job alone. Cleaning and vacuuming surfaces in your home is also important, along with keeping the pet brushed.