Yes, as far as signal is concerned, there is no problem putting these in a drawer. The wireless router uses radio waves to send and receive data ... wood will not interfere with it. Metal, magnets, led paint, thick concrete, wire mesh used in walls/flooring, non FCC approved devices ... those are the kinds of things that *would* interfere.
The main problem you will face putting them in a drawer is heat. Electronic devices need to stay relatively cool, which is why almost all electronic devices have vent holes in their casing. If there is enough air circulation ... like if you left the back where you ran the cords wide open ... then you could probably avoid that. Definitely don't put anything in the drawer with them; putting a sweater in there will be a death sentence for your devices.
The next problem you will have to face is dust. The more air you allow to circulate in the drawer, unfortunately, will mean attracting more dust to clog the vent holes and internal fans.
I would suggest, keep it in an upper drawer, leave the back open, and staple some screen to cover the hole to prevent dust from getting in. And, I would never let a service tech see what you've done :)