Never done this before and would expect that natural convection would have a tough time pulling through filters, unless you’ve got a big convective force driving it.
Here’s my 10 cents on how I’d approach it.
I don’t mathematically know where each formula would come from - but if you have your filter free convective airflow calculated you somehow then have the pressure increase that the convective transfer is “pushing” your airflow through with.
With that airflow and a specific filter selected, you can easily get the pressure drop of your filters from the manufacturer. Subtract that from the pressure boost of convection, and you will have a new airflow through the system.
However this airflow will then be lower, which means you have to recalculate your filter resistance, which will resist less because your flow decreased. This becomes an iterative process or Im sure you could set up some formulas to do this quicker.