YES! Drill press use of a hole saw means gravity holds the sawdust in the cut, and that's the main problem. Augers pull the sawdust out, as do Forstners. But, they convert the entire plug into chips, and that means they're doing more work.
I've had good performance from hole saws drilling horizontally, but the same hole saw is a trial to use in the drill press. Clean the scorch residue from your hole saw blade (lye or oven cleaner will do it) and try a slow-ish hand drill with frequent pull-out for dust clearance. If you must use the drill press, borrow an air compressor and blowgun.