With this post you should take my answer for a grain of salt because I do not know the specific facts about the hardware, I am merely making an educated guess.
I am thinking that Apple supplies the same batteries for their MacBooks with the same power output, so I guess that would mean it shouldn't do anything to the logic board other than maybe drain the battery quicker (since the newer logic boards use more power). I'm not sure which generation logic boards you're referencing (i'm assuming you're meaning the 2.4 core 2 duo and the 2.2 i5/i7).
If the battery has a different power output than what the logic board is made for, you can ruin your board (aka fry it) and/or ruin your battery.