If an ERC-20 Token Project Succeeds, Does This Really Drive ETH Price Up?

I have invested in Ethereum assuming that if lots of projects that are built around ERC-20 tokens succeed, that this is good for ETH and the price of ETH, but is this really true? I suspect that there is going to be some correlation over the long term but not as much over short term and ETH price will just be volatile for a while. Thanks!

– Thub