I was an MP for 3 years.
3 of the 8 guys I work with were MP's of some sort.
It isn't the best military job, look forward to 14 hour shifts. It might give you a taste of what being a LEO is like. Maybe you'll be able to decide if it is something you want to pursue as a civilian career.
Whether or not it will help, depends on the attitiude of the Dept. you apply to. But most Depts. will look favorably on honorable armed forces service. Don't overlook the National Guard or Reserves.
What would be more helpful is a degree in Police Sciences or Criminal Justice and an ability to speak spanish.
Of course if you have military service, a degree, and can speak spanish. Not to mention other skills like EMT that a PD may look favorably on, your chances of being hired get much better.
You would probably have an advantage the more you are over 21, PD's seem to have less favorable results when people without job histories, or life experience are hired.
As far as a PD saying we won't retrain an MP.......never heard that mindset.
Also be prepared to take a job in po-dunk, get some job experience before you can get to a more desirable employer.