Can a poorly-placed tower prevent a chest from spawning?

Solution 1:

In the Alchemical Laboratory, I have a tendency to plop a Slice n' Dice right where I marked it on the map here in red, on top of the chest spawn. I've found that it easily takes care of all the enemies spawning from the East door. The chest has always spawned, even with my tower right on top of the spawn area.

As long as you are able to touch the chest, you should be able to open it. Sometimes I had to shimmy around my tower a little, but I was always able to access the chest.

Based on this experience, I would say that no, placing a tower on top of a chest spawn will not prevent it from spawning, it will just make it more difficult to open.