i see no reason you cant. a hempy bucket is just a bucket with the drainage holes drilled some distance from the bottom to create a res that holds some water/nutes instead of letting it just drain away like in traditional pots. you wont need a air pump/stone.
I currently have one of my ladies in a 65 litre (17 gal) hempy style pot. the drainage holes are 3 inchs up from the bottom i filled with perlite up to the drainage holes and then filled with my soil mix (because im a dirt guy) but i see no reason you cant go a perlite/vermiculite/coco mix and use hydro nutes.