Are all erc20 ethereum tokens backed by some deposit of ether to a contract? If so, is there an overlap in the market cap of the current 24 billion in ether and the value of all the erc20 tokens?
Tokens are always counted separately - they are not considered as part of the Ethereum market. The opposite is also true: tokens do not include Ether market.
Tokens do not require any "deposit" of Ether. The only thing you need is some Ether in your account to be able to publish a token contract and that's it. After that you need Ether to interact (send transactions) with the token contract but the tokens are not directly related to Ethers in any way. In ICOs (token crowdsale) you can usually buy tokens with Ethers but the markets remain still separate - it's just about buying one asset with another asset.
You can for example have a look at https://coinmarketcap.com/ and see that Maker is #21. It's an ERC-20 token.