Lot of dapps use connect and don't need sign in (siwe), depends on what you're doing I guess
I think it sends the message if you have no wallet connected (asking you to confirm in the wallet, after accept the no-warranties message, but it do not send the signing message if you previously connected your wallet. Then, it just connects.
Why would you have to sign a message? The only reason sites do that is so that they can track you.
any action you'd take through etherscan is either an onchain tx, or just reading public chain data. so anything that needs the auth happens in a tx.
it doesn't care if you're faking it. if you don't actually have the private key, you won't be able to sign a tx anyway