That is an interesting question. My bet is NO. They made a special provision that the DoD would not be impacted by any shutdown.
I know that my DH, a GS with the DoD is being paid. He is attending the National Defense University in DC (DoD school) and was told on Friday before they broke for winter break that even if the govt shutdown they were expected to return on the 6th of Jan., bc the school is part of the DoD.
Point being the acronym for DoDMERB starts with the letters DoD. Thus, why my bet is NO.