Does generating an address reserve that address on the network then? Or are you just mathematically validating said address?
Once you have a validated unused address, How does one then get it into your wallet ?
It doesn't reserve it in the networks (at least I'm NEARLY sure it doesn't) until you add it to your wallet. What wallet are you using to store your addresses? If you are using a web-based wallet, it varies, but for Bitcoin-QT (the desktop client), go here for instructions:
https://en.bitcoin.it/wiki/How_to_import_private_keys