To ensure that you identify all of the locations that apply as other plugins may also filter disabled product out, go to your admin panel, tools, developers toolkit.
In the lower left corner enter: products_status
Select catalog in the dropdown, then search...

This will provide the list of files that and the line number of the code where that is used... From there you may need to make modifications to the code to obtain the desired result. Remember that if a returned file has the ability to be overridden with a template equivalent to copy the base file if it doesn't exist in the associated template folder and make the change there. The pages directory identified above is not overrideable, so yes the above modification should support product_info (product-general) products being displayed.