The utility of the Masters will depend on the kind of gap you put between the Msc and the MBA (work experience BETWEEN the MSc and MBA). From my experience seeing many students with similar profiles apply, the decision to apply for an MBA right after the MSc will be taken negatively by most admissions committees ('why go for the MSc at all if you want to get an MBA right after?').
However, if you can put in a couple of years of work in between the MSc and the MBA, it will show the adcoms that you did the MSc for a purpose - gaining more knowledge/experience in a field of your choice before going for the business management aspect of the MBA.
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