I believe something is better than nothing here. One of the biggest complaints against air filters is noise so maybe a good compromise would be to run them at full speed and full noise for a certain amount of time or something when nobody is in the room?
I too would like such a "shy" air purifier, but manufacturers always seem to go the other way: when occupancy is detected they increase the fan speed.
Best option IMO is just to get an air purifier with a good CADR-to-decibel ratio and then (again) size it correctly. A surprisingly good option is something called the Airfanta 3 Pro, which is basically like those wildfire filter boxes except it uses PC fans.
It is not expensive to run intake fans in the spring and fall seasons when active heating or cooling are not required.
Positive pressure systems are great, love 'em, but there's a quantitative mismatch in this case. Above ~1 ACH your HVAC costs will go through the roof (even with heat/humidity recovery), but for effective filtration you need 6-8 ACH to catch the larger dust before your lungs do.