Small particles and HEPA
Why HEPA-style filtration is the part people care about for pollen
For allergy-focused use, the important bit is particle filtration. HEPA filters are a common choice because they are designed to catch very small airborne particles efficiently. That includes pollen and other fine material that can keep drifting around indoors.
A HEPA filter is a mechanical filter. Air gets pushed through fine filter media, and particles are captured there instead of staying in circulation. So yes, the simple version is true: a purifier can catch small particles out of the air, as long as those particles actually pass through the machine while it is running.
The practical side of this is room use. If you want cleaner air in a bedroom, office or living room during pollen season, the purifier should be sized for that room and left running consistently, not only switched on once things already feel bad.