I don’t know, I have tried in-game and it just didn’t happen: if I put a chest below the hopper, then items reach the chest as expected, but if I put a drawer controller below the hopper, then items stay in the hopper and never get there.
In the drawers mod’s readme they say that hoppers are not supported because it requires a change in the hopper mod: https://github.com/minetest-mods/drawers/