You can print on a piece of paper a wallet and obviously you can't connect it to the web. To deposit money to any wallet you need a valid address tied to a private key. The address is unknown to the network until someone attempts to send money to it, then it is within the blockchain forever. You use the private key to sign the bitcoins tied to that address to another wallet.
To give you a visual representation:
The address you send money to is on the left and the key you need to access the bitcoins tied to the piece of paper is on the right. Blockchain's double factor authentication first encrypts your wallet and then also has an encryption for the private keys tied to the addresses within the wallet. You cannot sign for the funds in the wallet until you enter the second password thus preventing a hacked wallet from being useful.
Blockchain cannot decrypt the wallet nor the keys and thus the only possible failure event would be for their servers to crash and you losing access to your wallet. Thus you should backup your wallet often using their backup service.