I did that for years, before getting my floor standing drill press, but I didn't have the fancy cabinet for height adjustment under it.
I just used stackable boxes upside down on the floor with a few scraps of 2 by lumber on top to get the height adjustment that I needed if the work couldn't be clamped to the drill press table. A vertical board clamped to the front edge of the bench served as a back guide, because most of the time when doing this, I was drilling the center hole in lamp stock and this board helped me get the hole straight in the front/back direction. The side to side direction was easier because I could just use the drill press table set to 90 deg, as in the photo. It works, but drilling lamps is easier to get right if you spin the work in a lathe, which I didn't have at the time either. When you don't have all the right tools you get very good at finding alternate ways.
If you only have a bench mounted drill press, mounting it this way gives you drilling abilities that you wouldn't have otherwise, yet it still allows it's use with the adjustable height table as you would normally.
Central North Carolina