Probably not, but you will need to ask your employer. MDEA is not an IRS term and is not found in the IRS regulations.
I found a web site for Minnesota government employees that used the term MDEA to refer to a type of flexible spending account (FSA). In this case, an FSA is NOT an HSA or MSA, the rules are very very different.
You can read more here, or ask if you have a specific question.
"MDEA" appears to refer to an FSA, not an HSA, provided to employees of the Minnesota state government. As such, it goes nowhere on your tax return and would prevent you from being qualified to make an HSA contribution.