By "move your bitcoin" I guess you mean "sending the bitcoin to another wallet" ?
Yes.
Also, "sign your transaction offline" means "disconnect first, then import the private key into the wallet" ?
With just connecting your internet connection when signing the transaction, you don't really increase your security. For more security, you should import your private key into a wallet on an air-gapped device.
(how does it verify if there is no connection?)
You should have two wallets. One created with your private key on offline device and a watch-only wallet on an online device.
Here is a good guide.
How to spend from an offline paper wallet using Electrum