OTG works perfectly with a modded lapdock, with the keyboard, touchpad and 2 USB ports all interfacing via USB. The stock ROM even supports mounting and unmounting flash drives as shown by a screenshot in this post:
But I could never get it working with an OTG adapter. That same OTG adapter works fine on my Touchpad so thats not the issue. Its possible that the Droid 3 needs +5v Vcc to be connected, because when its on the lapdock its charging as well as providing OTG. This is different from my Touchpad which refuses to charge when in OTG and doesn't even need Vcc connected.
Motorola Droid Bionic
Stock 4.1.2 Rooted
CM11 4.4 Safestrap