Air purifier agains bacteria and viruses?
The aforementioned filter will filter microbes

Yes, it is routine practice to use microfiltration in labs to sterilize solutions from microbes. 0.2 micron filters will remove all typically-found bacteria most of the time, except for the odd bacteria here and there, though this is uncommon. 0.1 micron filters certainly remove all stray bacteria that may make it through upon a single 0.2 micrometer filtration. Here is a nice read on the appropriateness of 0.2 and 0.1 microfilters, which simply states that 0.2 micro filters are usually more appropriate since they additionally guarantee a better flow rate.

The aforementioned filter will NOT ensure filtration of viruses

These filters are not used, suitable nor effective for viruses, however. You ask specifically about the coronavirus. From a 2015 study:


  Coronaviruses are members of the Coronaviridae group and contain a
  single-stranded, positive-sense RNA genome surrounded by a corona-like
  helical envelope (Ryan 1994). The SARS virus genome consists of 29,751
  base pairs. Approximately 41% of the genome is GC base pairs while 59%
  is TA base pairs. Coronaviruses have a size range of 0.08-0.15
  microns; with a mean size of 0.11 microns (see Figure 1).


This means 0.1 micron filters will not protect you from these viruses. They may help you reduce viral count in the air, which may of course be sufficient, but this would not be an adequate measure in a biological safety facility.

The cost-effectiveness of commercial air-purifiers for biosafety vs. pollution

On a advice-related note: I do not think air-purifiers are going to help you in a cost-effective manner to avoid viruses (e.g. Rhinoviruses that cause the common cold, for instance), lest you stay at home all the time. You expose yourself outdoors, and carry plenty of viruses indoors on your body and in your respiratory tract; these will bypass your filtration system on the daily. Being healthy and lucky enough to avoid exposure to viruses outside the house is still the best bet. I think an air purifier has a greater potential to help with smog and urban pollution, those particles are typically larger than the diameter of most microbes.