I don't have direct information regarding the MEP's here, but I sure the MIL STD could be dug up on Google.
Generally, EMP testing would be done over specific frequencies and field strengths. EMPs happen in different stages (E1, E2, E3) and based on publically available reports, most consumer devices with proper EMI shielding would survive. Machines like cars or , in this case, MEP gens, would survive because the sensitive electronics are housed in a faraday cage-like box that attenuates the field strength of the pulse.
Devices likely to get smoked are things with antennas or long wires acting as antennas, which will concentrate the field strength to dangerous levels. Field strength is measured in Volts/meter, so more meters of wire equals more induced voltage.
What I can't say for sure is if that EMP rating applies with power wires hooked up or not.
And yes, the batteries will be okay.