Any expenses that were not paid with tax-free dollars can be used as a tax deduction.
However, I don't think you understand the point of the HSA. If you deposited $4000 (or $3350 if it is a single plan) and then withdrew it the next day to pay the out of pocket cost, you would still get the tax benefit. And because you have until April 18 to make a 2016 deposit, you could deposit the money today, and withdraw it tomorrow and put it back in your account, and consider that it was used to pay your bills, and get the tax benefit of the HSA which will probably be a bigger benefit than the deduction.
