Extreme Problem with AppleCare (Does this mean I have a free phone?)

I had a problem with my iPhone's battery back in August, I had AppleCare so I requested a repair. I paid to have a temporary phone sent first, but it never arrived. Apple said it did, but it never did. And then they threatened to charge me for it many times but I never got it. Even the signature on the FedEx delivery was not my name. They tried to charge me, but luckily they only had an old credit card number to it did not process. I thought all this was over until last month I received the phone, still dated from August (never went back to Apple that whole time) I have no idea what happened, but since my claim is canceled (and my iPhone battery is fine now, not needing repair) I have this AppleCare Phone. I want to use it as my own phone and sell my other (to save for a 3G iPhone, I can use in Japan), but I am afraid that when I put in my sim card and it activates, it will alert Apple of the serial number, that is supposedly missing (although they tried to charge for it?). Is the serial number sent to Apple when you sync the phone (with a new sim for the first time)? Any advice would be greatly appreciated! Thanks a lot!!! (^_^)