Is an Ionizer Air Purifier effective against birch pollen?
It's hard to tell from the product page, but it looks like this is just an ionizer, with no fan or filter. If so, then all it does is emit ions; it doesn't remove anything. The theory is that it will charge particles (e.g. birch pollen), which will then attach itself to nearby surfaces, thereby cleaning the air. Unfortunately, these are more effective at generating ozone than actually cleaning air, and ozone, whilst very helpful high in the atmosphere, is very bad at ground level and in the vicinity of people (e.g. lung damage).

This is different from a true electrostatic precipitator, which emits ions into a fan-driven air stream, but immediately collects them (and any ionized particles) on plates parallel to the air stream. These work very well, but are larger and more expensive than simple ionizers, and emit some ozone as well.

I found an article on Effectiveness of Home Air Cleaners in Reducing Indoor Levels of Particles, sponsored by Health Canada. It compares various ways of improving indoor air quality. Another useful article is a Consumer Reports overview of air filter types. Based on these, a standard HEPA filter (thousands of models available), or perhaps a portable electrostatic precipitator (I couldn't find any) would better meet your needs.