so I guess you have to be online for the software to check it is creating a unique wallet address no one else has then I you just go online periodically just to 'sync' up with the network and see your balance. Is that correct?
There's no checking that your address is not in use. You just rely on the fact that there is a huge number of addresses so the potential for overlap is very small. If you're lucky enough to generate the same address as another person then that's great, because you can steal all their coins.