Deductions & credits

A literal reading of the law (Section 223 of the Internal Revenue Code - https://www.law.cornell.edu/uscode/text/26/223) would suggest, "no". 

The law allows for 4 situations in which you can pay for health insurance premiums from your HSA:

(i)
a health plan during any period of continuation coverage required under any Federal law,

(iii)
a health plan during a period in which the individual is receiving unemployment compensation under any Federal or State law, or

(iv)
in the case of an account beneficiary who has attained the age specified in section 1811 of the Social Security Act, any health insurance other than a medicare supplemental policy (as defined in section 1882 of the Social Security Act).

***Notes***

(i) refers to Cobra coverage.

(ii) refers only to LTC.

(iii) requires that you qualify if you are actually receiving unemployment benefits.

(iv) refers to people 65 and older.

So what you need to do is go to your benefits co-ordinator and see if (i) or (iii) can apply to you, since I do not know the details of what your "leave of absence" are. Show your benefits person the wording of the law to help him/her understand what the requirements are (this can be a bit different than the IRS instructions).