My experience may not be directly relavant to many of the members of the forum as I am in South Africa, not Europe or America. Perhaps attitudes are different there.
I did an MBA about 15 years back - 2 year course - after a few years in engineering. I learned a tremendous amount - as far as I was concerned it was a great learning experience.
BUT: When I went job hunting, the local aircraft industry made it quite clear that I was no longer welcome. To quote the HR people from two major companies:
"Engineers should stick to engineering, and leave business to people who know what they are doing"
"Any combination of business and technical qualifications automatically makes you unemployable in this industry"
I ended up working for a non-aviation company in corporate finance and strategic planning for many years, before returning to aviation. The company that employed me back in aviation were at considerable pains to tell me that they had no use of my business skills, and were purely employing me as an engineer. Didn't stop them asking me to manage a department shortly afterwards....