Firstly, be careful when using car batteries as they are often designed for outdoor use and your results may differ from using UPS batteries. Obviously APC can only recommend using official APC RBC's. I have not actually tested this scenario, but I do believe that the UPS will show "battery disconnected' (flashing replace battery LED) if no battery is connected internally. Either way, if you are using a custom external battery setup like that, your runtime will definitely not be estimated properly.
Unfortunately I can't really provide much advice on this subject as I cannot recommend the use of batteries such as these; we of course haven't tested scenarios such as this.
Perhaps someone who has tried something like this can comment, and provide suggestions. If there are any specific questions about the UPS, let us know and I'd be happy to help with what I can.