I don't have any experience with this, but I don't see why this shouldn't work fine with a battery box. The box will just provide more power to your mics and pass the mic signal through to the shoe interface.
My son sometimes uses a little SoundPros preamp and AT943 mics into a line-in jack on his Sony digicam (not sure what model he's got) and it's a big improvement over the integrated mics, but a preamp might overload your mic-in interface.