Leah Binder, writing in Forbes on line ( see here) argues that the answer is "maybe" at least as regards what she calls badly designed programs. She draws from a book from Al Lewis and Kiv Khanna entitled "Surviving workplace wellness".
Practicing internal medicine and pulmonary disease in the late 1970s I had not heard the term "wellness" until I was approached to consult for a large petrochemical company who believed they had a problem with some type of occupational lung disease at one of their facilities. ( The term risk factor was new to me as well)
Later while working part time at that company I sat in on a presentation from a consulting firm who was selling employee wellness programs.They showed slides with huge alleged savings from the detection of early disease in the employees. One cynical older HR person said yes that maybe be true but if we save those lives while folks are working will we not be shelling out more money in longer retirement payment because if we have both a health insurance program and a retirement program we will be paying now or paying later.
That argument aside Lewis and Khanna make a persuasive and humorous case for shelving most of what passes for employee wellness programs, which by the way are encouraged by Obamacare giving us reason 962 for never having passed the biggest crony capitalism con job windfall ever.
The authors tell us that the "sum of value created when an employer plays doctor" can be put in a very small footnote,
get off your butt
Their analysis resonate with the impression I had years ago .The difference is they have data to support their conclusions.