This seems like a question that can be answered with data. My gut feeling is no, based on how bankers kept their golden parachutes intact during the Great Recession, but maybe I'm wrong.
Maybe I've worked at all the wrong companies but in my experience any comp that's based on "data" will be gamed until it's meaningless. There is no "data" because reading impact data is often like reading tea leaves.
Frankly, what I think is going unsaid here is that corporate executives make a disparately large amount compared to the people who do and plan the work. While executives can make a great difference, so can a great manager or a great engineer. I wish we'd see executives as just another role, taking on different tasks rather than something substantively more valuable when it's not, especially in large orgs.
At some level of compensation, the only people motivated to pursue it are sociopaths. Are these the people you want running your company?
[1] http://si.wsj.net/public/resources/images/OG-AE821_ExecPa_NS...
My point was just that you can probably tease out some idea about the relation between executive compensation and company performance from available data. Personally I would not even consider shareholder return to be a good metric to begin with, I think companies should be judged by something like customer satisfaction as this is what companies are for, satisfying the needs of customers, not making shareholders rich.
So, not much benefit even if we blow the lid open and show a much better way to make more money. That is important for a publicly traded company, but far from their only consideration.