When is the reduction - or rather the translation of a problem - to QM, possible and productive?
Sometimes, it is impossible. The planet's orbit stability problem isn't even translatable to QM, at all. Because QM doesn't do gravity.
I doubt it is always productive, even when possible. One could translate the game of tic-tact-toe to QM. But what's the point? A simple look-up table would do. Can we translate the look-up table optimization to QM? Maybe, but it would hardly give us any new insight in tic-tact-toe game.
It has implications for morality if the existing definitions of consciousness turn out incorrect or incomplete. It has implications for singularity technologies of mind uploading and cryonics revival if a theory of consciousness can be extended to predict end-of-identity. It's also simply interensting in its own sake.
Max Tegmark publishes a preprint of a paper arguing from physical principles that consciousness is “what information processing feels like from the inside,” a position I've previously articulated on lesswrong. It's a very physics-rich paper, but here's the most accessable description I was able to find within it:
The whole paper is very rich, and worth a read.