Can I work for the Military with RPI status?

Absolutely.  The Border Security, Economic Opportunity, and Immigration Modernization Act of 2013 stipulates that any alien granted the Registered Provision Immigrant (RPI) legal status will be eligible to enlist in the United States armed forces.  It is important to remember that in addition to having the opportunity to serve the people of the United States, those immigrants who meet the requirements of their service, and subject to a few other conditions (the Military may have its own requirements with regards to misdemeanors), are put on a fast track to permanent residence and naturalization.  They also apply for these benefits through slightly different channels and some of their fees can be waived (yes, it is pointless to conduct a background check on a serving member of the Military because they are being watched any way).