We appear to discussing "causation versus correlation."
Your organization,
@cubix rube , may see a correlation between proper hand hygiene and absenteeism rates, the latter of which might have an impact on your production numbers, but is there a causal relationship between hand hygiene and absenteeism?
To be fair, I don't think anyone here can answer that question for you since we are not privy to your pre-hand hygiene data nor your post-hand hygiene data. Maybe it will have an improvement for your organization whereas it would not for another.
If you want to prove that than your organization's hand hygiene initiative has had the desired results, you'll need that data. No data and, well, maybe absenteeism rates decreased because oranges went on sale at the grocery store and everyone has plenty of Vitamin C coursing through their system. And if the rate doesn't change, then, it's likely the initiative hasn't had the impact your organization was hoping for.
And if the rate remains the same or gets worse...well...I have to ask...has your organization had a discussion with the actual folks who contribute to the absenteeism rate? Has there been an effort to understand why folks don't show up? Is it always because they're sick? Or are they "sick?" On the flip side, has there been an effort to understand why people actually show up? What drives them? Can something be gleaned out of that to help inspire others?