It won’t work that way for sure. The “&ignore_op=1” additional parameter for the header search is mandatory. The page that it redirects to will recieve the $_GET[‘ignore_op’] variable, thus the catalogue instance as well. So it will recognize that this particular call doesn’t need filtering. If it’s not there, it won’t know to ignore filtering.
Any subsequent filtering with the catalogue search will not send this query parameter again, thus the filter is active then.