I'm new to the site, esp. posting...but do have some experience on this question...so I'll share what I've learned.

A fishing buddy and I are in the process of learning how to build crappie condos, and thought that we'd better check ...we're working Beaver Lake.
I called the local COE office, and received a prompt call back for my message left. The fellow on the other end said no permit was required for structure of natural materials, Christmas trees, brush and such, but that if something substantially larger/different was being considered that they'd probably want to see some plans or have an opportunity to say go/no. As we're planning to build 'em of pvc, I asked if there was a problem in using that...along the lines of the Bill Dance Porcupine design, and he said no problem, that game and fish has been putting several of those out too. The guy gave some generally helpful advice regarding water depth and thermocline and current water level being down... and I got a generally favorable 'feel' for the whole episode.
Hope that helps.