You're going to find that isn't stable enough. You can't hold it tight enough to keep it from walking, the cheap chuck wobbles, the depth stop isn't precise enough, etc.
For the first couple of Harry Williams games I did, I used a portable drill stand (like a really bare-bones drill press that you lash your own drill into) and spun it around backwards so it had infinite reach, and then bolted it to a really big thick heavy board, then clamped that board down where needed on top of the playfield wood. (See attached picture)
It was a pain in the butt to align precisely, sometimes the dimensions involved didn't allow me to change bits mid-operation without unclamping the thing, and despite all the solidity, it *still* skewed under the pressure of trying to bore through playfield wood. That stuff is hard!
So I bought a good used radial drill press on Criagslist. Unlike a standard fixed-jaw drill press where you need something the size of a car to get enough depth to reach the center of the playfield, a radial drill press slides the head horizontally, allowing enough depth if you buy a big enough one.portable_drill_stand_01 (resized).jpg