I have tried that too, but never really saw the value in that, although that could be because my lack in tasting skills.
I’m grinding fairly fine (1.1 in the Aergrind), which seems to clog up the paper
filter to such an extent that dripping is very slow. I also stir a lot to make extraction a bit faster, so I would say that I haven’t had trouble with extracting enough in the upright configuration.