I know this isn't quantifiable, or the answer you're actually looking for, but my wife's happiness with me increased exponentially after I started using GTD. I remembered and completed all the things she asked me to do.
Now, from a vocational perspective I keep track of all my projects and have counts for annual completed project totals for about the last 7 years. After I started using GTD at work, the projects I was able to complete annually went up an average of 28%. A simple example, but one that made me realize GTD seemed to be improving my productivity. Subjectively, it's made me less stressed at work and able to handle more projects simultaneously. My co-workers notice that even though it may take me awhile, I do eventually follow through on my commitments.
I think you would need to find already existing data sets prior to a GTD implementation in order to experiment and measure results. For instance, collecting employee satisfaction surveys (
how do you rate your job satisfaction from 1 to 5) or lead time (
time a request or idea takes from initial stages to completion) would be two very simple examples of data sets to measure against after a GTD implementation. But the first step is in finding any existing data you already have to determine how useful it would be, and how you would use it to compare post-implementation.