I think Opera mini can be installed in nook without any problem. But it is unusable in nook.
With my testing, android app can be installed in nook without problem, I have installed a couple of offline RSS reader clients, all of them can startup normally.
Because currently nearly all android apps are designed for phone with touch screen, but in nook only part of screen is touchable (app treat e-ink screen and below touch screen as a big screen), The biggest issue is input, so far you have no way to control most apps, except you use VNC.