A particulate sensor can be used to cheaply monitor the appropriate size range for pollen. Of course, it just senses light scattering, so other air polluting particulates of a similar size will be indistinguishable. Large particulates greater than 10 - 100 microns in diameter are likely to be pollen in an outdoor environment, but they can also be combustion related particulates. More information can be obtained from sensors that measure light polarization, which may allow one to differentiate pollen from other particulates of similar size.
Depends on what you call 'reasonable', but the answer is likely 'no'. The 'Air Quality Egg' was a kickstarter project a year and a half ago, but they failed to produce a calibrated device. Measuring particles is doable, it's the calibration that is the issue. Most of these sensors don't show useful measures for air pollution, although most claim they do.