Yes, the books you purchase are tied to your AdobeID. You can erase the activation in ADE by hitting Ctrl-Shift-D (Cmd-Shift-D Mac). This just erases the activation information and does not give you an activation back.
Your Nook and Digital Editions must be the same. I think you can reauthorize your Nook. I found the Nook desk very helpful at my B & N.