You MIGHT-- I emphasize "might" -- be able to push a plastic wad down if you put a short starter into the wad, and give it a big WHACK, but anything more than Modified choke will probably produce a torn plastic cup. You will have to push the cops past the chokes, before pouring in the shot.
And, you definitely need an OP wad under that plastic shotcup, regardless of chokes. Otherwise, the Black Powder burns the base of that wad, which is one gauge undersized( for cartridge guns) and deposits residue in the barrel. That will make putting subsequent wads down the barrel more difficult, and eventually, impossible.
It helps to grease the bore of the barrel After seating the OS card on top of your shotcup. Just grease up a cleaning patch, and, using a jag on your rod, run the patch down and out the bore of the shotgun. The grease will allow the plastic cups to slide over the bore, rather than rub plastic off on it.
I can only assume you are hunting ducks, if you are using #3 steel shot. That shot is not large enough to reliably take geese, except within 20 yards, and then you would not need the chokes in your barrels.