There shouldn't be any issue with a wooden motherboard tray. Or if there is, keep it quiet, before my tray hears about it.


No real disadvantages come to mind. Similar to a non-metal case, you have a potential EMF issue, depending on whether there's anything sensitive nearby. I understand that some jacks on the back of the motherboard need the metal tines grounding them, although I'm not sure about the specifics, since I haven't run into issues with anything I've plugged in yet.
If you're trying to put it in a case, you'll have trouble getting the wood thin enough to have the proper height so that the expansion cards slot in properly, although this is obviously a moot point on an open bench.
Edit: Oh yeah, can't think where it was, but 3oh6 posted a pic of his benching "board", and if memory serves me right, it was completely metal-free. Not styrofoam free, however.