It probably depends a bit on how big the chest of drawers is and whether there are any other appliances next to it that can get warm, but I personally can't recommend it.
I have the Dream Machine on an open shelf and it runs at a constant 61°C without you hearing the fans. I think 61°C is rather warm compared to the Asus AC-RT86u I had before. And during certain situations, such as installing updates or other testing, the UDM can get much warmer and louder.
The device actually looks quite OK, so it's almost a shame if it stays hidden in the dresser.