Yep sulphuric acid, at least the concentrated stuff, is a strong dehydrating agent and will char all wood products to a greater or lesser extent. Battery acid as it dries will also tend to attack wood even if not at battery concentration.
I would expect a particle board to be particularly at risk so I agree that marine or WBP ply would be a slightly better choice. The secret is of course not to spill battery acid in the boxes!
GRP is acid resistant so boxes lined with GRP should be acid proof and acid tight, but that's been said already. If you don't gel coat them stand the batteries on some heavy polythene sheet to stop them sticking.
-------------------- Old Chemists never die, they just fail to react