A600s don't have batteries on them. The Amiga that had the big leaking battery problem is the A2000. A1200s and CD32s are renowned for their leaking capacitors, which have less acid to cover the motherboard when they explode than a battery, but can still do serious damage if left unchecked. I'm pretty sure A600s would suffer from the same problem, being made of surface mounted components and covered in caps like the A1200/CD32. Some older A500 and A600 memory expansion boards have barrel batteries like the A2000 and these can explode too. I've seen many dead A500s because the battery on the memory card exploded.
A600s are good though, and easy to expand with new hardware available now. A1200s have it all, already. Everything the A600 has got, and more, but usually at a higher price, and it won't be long before you crave a RAM expansion or accelerator with extra RAM on it, which at the moment can't be bought new. The A600 has the A603 1MB (for a total of 2MB ChipRAM) expansion available to buy from
www.amigakit.com and hopefully soon the A608 8MB (FastRAM) expansion from Zetr0 will be here. Unless someone out there makes a cheap 8/5.5MB/RTC RAM expansion card (preferably with automatic or software switchable 8MB or 5.5MB modes for PCMCIA usage) for the A1200 some time soon, the supply of available second hand RAM and accelerator cards is going to dry up and prices will continue to skyrocket.