Aladar, you need to clarify your gear chain better.
Right now, you're running: a pair of CSB > Core Sounds bbox > Sony MD.
Like this, right?
But what about this other battery box??? Is this something that came with the Sony, or some third party gear? If you can change the levels with this box, it's technically not a bbox, but a preamp with adjustable gain. What mode/make?
So technically, you want to know if you can throw this pre into the chain, but it only takes XLR in?!
Sure, you'd just need an adapater cable inbetween: 1/8" female > 2 x XLR out
But IMHO, you would probably spend that money better if you buy another recorder than the MD, rather than buying an expensive cable and be stuck with a sub-par rig.