Ionic air purifiers are not "air ionizers." They are "particulate ionizers." They ionize the dirt particles and then use potential fields to catch them on a plate.
There will be very little ion emission from these things. The mean free path of ions at atmospheric pressure is exceedingly short, and ion/molecule reactions are fast. Neutralization will occur fairly quickly.
The health problems come from the emission of ozone, O3. However, even with that you have to be pretty close to the source to get any before it reacts away.