No. Box 12, code W is only for employer & pre-tax employee contributions to a health savings account (HSA). It is *NOT* for health insurance premiums, HDHP or otherwise. Pre-tax health insurance premiums and medical flexible spending account (FSA) contributions are deducted from actual gross to arrive at W-2 Box 1 (and other boxes), but they do *NOT* have to be reported separately on your W-2. (Your employer may put them in Box 14, but it's not required. Contributions to *dependent care* FSAs are reported in Box 10, but not *medical* FSAs.)
