Generally, no, but there are 4 exceptions.
The accountholder can pay health insurance premiums from the HSA if the accountholder is:
1. Receiving federal or state unemployment benefits
2. Has health insurance that is continuing coverage under COBRA
3. Paying for coverage for a IRS-qualified long-term care plan (See IRS Publication 502) and,
4. Paying for Medicare premiums once the account holder is age 65 or older.