Your Ethereum address already "exists" on the blockchain before you generate the private key to it. Anybody can send funds to it, and you can check the balance using a blockchain explorer like https://etherscan.io/ (which is the way all people should do it since you don't have to use any sensitive information for this).
You're correct in thinking that you need to be connected to the internet to see the current state of the blockchain, and thus the current balance. But it's perfectly safe to use Etherscan on your normal online computer to do this.
For sending transactions out of the address, you generate the transaction via MEW on the Tails drive, drop the signed transaction data onto a secondary drive, move it to an online system, and broadcast the transaction.
It works similarly to a hardware wallet where the unsigned data goes into the secure system, and the signed transaction comes out, but all the sensitive information stays secure.