If you haven't torn any copper traces on the motherboard, you should be fine. You're better off without the battery. Do you need an Amiga to know what time it is?
Check the area around the battery for corrosive residue. The battery on my A4000 left a circle of corrosion that went far beyond the battery. It extended as far as the sim sockets. Any green fuzz you see around where the battery was is a sulfated copper that used to be part of traces on the motherboard. I removed the battery on my A4000 and then cleaned up the motherboard, first with a mild baking soda solution to neutrilize any acid residue and then with a damp cloth to remove the baking soda. I carefully removed the remaining green fuzz and checked all the circuit board traces under them. I had to clean the first sim socket with a small wire brush--the sim as well. The A4000 motherboard is a lot more tightly packed than the A2000 motherboard and the battery is located in a much more vital area so the potential for serious damage is far greater.
The proof of the pudding is, of course, eating it so after checking everything out visually, fire up the system and see if it works.
