Either way it sounds like I won't ever get the BTG but still interested in when the BTC became 'mine'.
Well, technically the BTC will become yours once you've withdrawn them to a wallet of your own, meaning you, and only you, have access to the private key that holds the balance.
That being said, while I'm not sure on how Coinbase functions internally, my educated guess would be that the BTC you bought aren't yours until they show up as part of your account balance. But yeah, I wouldn't get my hopes up on Coinbase supporting BTG.