at an overworld lava lake we used water to make it obsidian then the quarry mined the top two layers of it (always using water to turn it into obsidian once we get to the next layer) and everything below that two layers is just being ignored... that's below those 2 layers:

Yeah the quarry won't auto-update itself after every block change, but if you shift+right click the quarry with a wrench it should recalculate its internal block scanned cache and mine the obsidian.