The only "computer-in-a-keyboard-case" Amiga model with on-board motherboard battery was the A500Plus.
I had quite the scare with my A500+ when I first heard about the leaky batteries. I instantly popped it open, and there was the battery, all furry and bulging! :-o
It actually started leaking when I was snapping its tiny legs off, man that things was ready to go.. I replaced it with a similar battery. I shoulda put it off-mobo but I could still do that.
I love that machine! The A500s are built like bricks compared to the other wedges, you can just feel that when you pick one up.