Yeah, this is exactly what it's designed for. Pet allergies are triggered by proteins in dander (skin flakes), saliva, and urine, not the hair itself. The HPA300 uses a True HEPA filter that captures 99.97% of airborne particles as small as 0.3 microns, which includes pet dander.
For it to work effectively, you need a strategy. Run it on the highest setting when you're not in the room to do a major clean, then keep it on a lower setting for maintenance. Put it in the rooms where your cat spends the most time. It won't remove dander that's already settled on surfaces (you need vacuuming for that), but it will significantly reduce the airborne levels you're breathing in.
HEADS UP: Since 100% of U.S. households have detectable levels of cat and dog dander, consistent use is key. Also, remember that no air purifier is a complete substitute for other measures like washing bedding frequently and keeping the cat out of the bedroom if your allergies are severe.