There are 2 major theories about credentials: human capital theory and signaling theory. Under HCT, certifications, degrees and licenses show that you have accumulated a credible amount of knowledge, and demonstrated it to a third party. Under signalling theory, certifications and licenses are signals to show to others that you are different. One interesting comparison of the differences of HCT and ST is The Career Consequences of Failing versus Forgetting.
While many in IT have a disdain for degrees, certifications and licenses, not everyone else in the business world feels the same way. One interesting dissertation (your local university library might be able to get for you) is titled "Hiring and Inequality in Elite Professional Service Firms". This dissertation interested me in that it was a sociological survey of some top consulting companies and it measured how they actually selected candidates in contrast to how they said they selected candidates. The mismatch could only be explained in terms of signals and not in terms of human capital. You may know just as much as another person, but the one of you that passes some hurdle signals to prospective employers that the hurdle passer is the better candidate. This is because hiring a person is trying to predict future behavior/success with limited information, and many people use signals as heuristics.
That being said, the way you phrased your question, you are looking at certifications from the viewpoint of the streetlight effect:
The fundamental error here is summed up in an old joke scientists love to tell. Late at night, a police officer finds a drunk man crawling around on his hands and knees under a streetlight. The drunk man tells the officer he’s looking for his wallet. When the officer asks if he’s sure this is where he dropped the wallet, the man replies that he thinks he more likely dropped it across the street. Then why are you looking over here? the befuddled officer asks. Because the light’s better here, explains the drunk man.
If you do collect this data, I suspect that you will find it useless for project appraisals. If you manage to find a statistically significant correlation with project success/failures, then you have the material to write a number of academic journal papers.
For a decent text on metrics used in software, I recommend you read Software Metrics. I've used this in a university course on metrics, and it has a number of recommendations on what you probably should be measuring instead.
Let's assume the company will pay any certification exam to whoever wants to submit to it.
In the company I currently work at, passing Microsoft and Oracle certifications gets you $500 (per test) plus the cost of the test and study materials. Even with such a large bonus, I am the only developer taking advantage of the program. Our company is a "partner" with both Oracle and Microsoft, so it is in the company's financial interest to have employees pass the certification. When I've asked the other devs why they didn't feel like earning an easy $5k/year, they stated a number of reasons from "I don't have time to study" to "$500 isn't enough". The resistance to certification is not something that you will be able to overcome merely by throwing money at the problem.