If you're referring to transferring from one address to another, I believe you'll still be able to see it on any explorer even if you use an offline wallet.
You are correct. The network has no concept of which addresses happen to belong to hot wallets or cold wallets, which wallets are currently connected to or disconnected from the internet, or even if an address is not part of any wallet at all and no one knows the private key. All transactions are public, regardless of the addresses involved.
I don't think people consider them as "lost crypto" too.
Also correct. You cannot say that just because an address is dormant that those bitcoin are lost, and the 4 million or so number that gets thrown about various blogs is a complete guess. The number of provably lost bitcoin which can never be spent due to technical reasons is very small, around 2,828 BTC.