I'm learning something new! Interesting.
So hypothetically if I have for example, 5 bitcoin in a personal wallet such as blockchain.info or some other private wallet, will the new BTC altcoin appear in this wallet as well?
Yes they will but they will not be visible immediately. If you own x amount of bitcoin in a wallet over which you have control of private keys then after the dork has been resolved you will have equal amount of the forked altcoin in that wallet. But to claim that amount you have do something yourself. Like for bitcoin cash claiming Electrum released the Electron Cash wallet and there is a method to claim BCH using that. Several other exchanges and casino bankroll investment sites like crypto-games asked users to put in BCH wallet address to claim their BCH if they had invested any BTC in their bankroll.
I don't get what you mean by: "It's not visible immediately."
If bitcoin ends up forking the whole blockchain will be copied until the point of the fork. So as soon as it forks your bitcoin will also be on the forked chain. But in order to claim them you need to wait until a safe wallet is available, not to mention the risk of replay attacks.