Yes, it will work… I’ve done the same with the old enterprise stuffer since it comes with a strainer basket. but I’ve also used my 7# vertical manual stuffer, here’s the process:
I tried cheesecloth but it’s not strong enough. Go to fabric store and ask for wedding dress material(2 yards)… i know…but it’s very strong and let’s the juice through. i cut 18"x18" or so squares of the material, ran the quartered apples through my grinder on the largest plate i had into a “China cap strainer”( used in restaurants to filter fryer oil) sitting on top of a large pot. Let some of the juice come out there then fill up the squares with the pulp. It works best when i pressed them one at a time in my vertical stuffer worked well, just be patient and take your time. Not as good as the Enterprise but didn’t take long to press a gallon of fresh cider with my own apples(not sure the ratio of apples to gallons). If you let it sit in a large pot or jug overnight then skim off the top and filter it will be less hazy but i didn’t mind/couldn’t taste the fine pulp.
One of my holiday favorites is putting a gallon of cider in a crock pot with some cinnamon sticks or mulling spice and serving it with salted caramel vodka, warms the soul…Good luck!