**No.**  A deployed contract on a blockchain does not get deleted when Geth's console is closed.

Restarting the Geth Javascript console requires variables, like `greeter`, to be re-initialized because the Javascript variables are in memory only and not persisted.

One thing that can help:

> Geth has support to load custom JavaScript files into the console through the --preload argument.  This can be used to load often used functions, setup web3 contract objects, or ...

>`geth --preload "/my/scripts/folder/utils.js,/my/scripts/folder/contracts.js" console`

For more information, including other ways to use Geth's console, see:
https://github.com/ethereum/go-ethereum/wiki/JavaScript-Console

Tools such as Truffle make ongoing contract development easier, for example Truffle saves contract addresses and ABIs, so that as @Rob mentions, re-initializing in Truffle, when needed, would be a simple `greeter = Greeter.deployed()`.