Any advantage to getting a free MS in Finance while working for gov't before going back to MBA for IB?

I'm considering taking a grad program in Denver (where I work and would make it more practical) that my employer will pay for while I'm working. I want to go to a top MBA school after some WE but I'm looking at both an MS in Finance or possibly a terminal MA Economics degree right now.

The director of the program got his PhD in Finance from U Chicago, so he could possibly be a good reference for MBA school.

I am working so I'd be taking like 2 classes/semester, and probably at night.

BTW I'm from the east coast and I understand the prevalent bias in the NYC market. I basically don't want to "HURT" my chances of getting into a top MBA school (because of the whole essay - why MBA, why here why now?). I'm stuck in the area for at least the next three years due to my employment. Its free money for school and I just figured I should take advantage of it.

I'm also looking at a terminal master's in mineral economics to (possibly) help set me up for a trading desk position in commodities down the line. The fact is schools where I work are regional.

It may keep me up on the theories going on in finance/econ and graduate level econ may actually help my quant side, so there may be some benefit, regardless of the quality of the school. The other side of me says that having a degree from any of these schools may actually mar my record and hurt my chances at a good B-School after I'm finished with work here.

I know this is not a high-ranked program or internationally known, but it could help me learn more especially at the grad level degree about economics... Any insight?