Yes, just cut the metal bits off that are holding the battery to the board, it's quite easy to do.
Can it cause a mouse problem? To be honest, it can cause all sorts of problems... but even if it doesn't cause this problem, it'll cause others.
It is repairable, though - I just repaired an A1500 with battery damage which didn't boot at all (black screen). These machines you can usually repair one way or another with a skilfully placed wire and a copy of the schematics!
