Assuming I was lucky enough to mine the exact same address, could I get the privkey?
Yes, if you got the exact same address, then you would have one of the 7.9 X 10
28 (on average) working private keys for that address.
wait im not quite sure i understand, are you saying that every bitcoin address has more than 1 private key associated with it? I've always thought it was 1private key that links to 1 address