Marines have their own MP/SP types as well. Normally, they aren't the most tightly sprung individuals out there.
I knew one MP who would beat himself with a pool cue to "desensitize" himself to being struck with blunt force weapons.
Their own Battalion though? That just sounds weird.
When I was aboard ship, all Marine Cpls and Sgts would be assigned extra duty when in port. they would take turns as Shore Patrol to control any Marines and Sailors who were out of control during Liberty. Also they would be assigned Brig watch if there were any Marines in the Brig.