It depends.
How is the pass-through reported on your W-2? Is it part of the amount that is with the code DD in box 12 on the W-2? Do you have a code W in Box 12, and if so, is the pass-through amount part of the amount with code W? Yes, you will probably have to ask the payroll department.
Code DD shows the amount of health insurance premiums that you and your employer pay towards your HDHP policy. Code W shows the amount that contributions that your employer and/or you through payroll deduction make to your HSA.
In the simple case, anything that goes into your HSA (from any source) is an HSA contribution, so the answer is "yes", but now we have to figure out how it gets reported on your tax return. Please answer the questions in the first paragraph and we'll take a look.
[Edited 1/13/2023 } 9:07 am]
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