retrofit an installed HVAC system
Yes, of course that could be done but you'll likely be looking at some significant ducting work.  The air return, that normally comes from the living space will need to be re-routed and brought in from outside.  Since that will create back pressure on the air handler blower, you will also need to duct the living space to the outside.

Often air-to-air heat exchangers are used in cases like to to minimize losses.

But to your point, I don't believe this is going to be in any way effective in removing COVID-19 virus particles from your space.