Don't think that's legal.
> What if employers require their employees to do this much like drug / background checks?
Also don't think that's legal.
We already have employers requesting "voluntary" disclosure of health information (e.g., cholesterol check) as a condition of continuing group insurance coverage. Since it's illegal to require this information, they make it voluntary - but anyone who opts-out also opts-out of a hefty premium "discount". In reality, the "discounted" rate is closer to what employers would expect to pay for comparable group plans, while the non-discounted premium is high enough that 99% of employees line right up to have their blood drawn by the visiting nurse (conveniently stationed in the conference room down the hall).