Technically you can, but as a practical matter like everybody has said, no.
I rebuilt my PHD to fit on my quick hitch. It only works because I have a hydraulic toplink. With the 3pt all the way up, the toplink will make the PHD lift the rears. Only works for the fist bit of the hole & really raises the pucker factor if you actually raise the rears really (sitting on the front axle pivot pin & a spinning PHD isn't even close to stable or smart).
Brand new JDs have an optional 3pt down pressure kit that will do 400lbs of down pressure or something, as well as a very few other really old tractors. Not sure there is much value in it beyond a PHD or possibly starting a cable plow or subsoiler. Generally you'd loose an equal amount of traction, which is more valuable. A PHD is the only impliment i can think ofwhere you aren't moving & would benefit from down pressure.
For everything else get the right heavy implement for the job.