Unless we communicate what Bitcoin's potential problems are and why alt-coins solve them then yes it's possible Bitcoin going down could take all of crypto with it in the short term.

What are Bitcoin's problems?

It is the first iteration of an entirely new technology that has been unable to rapidly adapt to innovation and challenges.

1. Volatility - 100 000+ merchants selling in BTC, nearly all dumping immediately for Fiat. Solution: Currency stable BitAssets like BitUSD

2. Inflation - New coins coming onto the market in times of low demand can depress the price far more than the inflation rate. Solution: Low/No inflation alternatives

Bitcoin has also become quite centralized around mining pools & BitPay type services which has been solved by more decentralized alternatives and transactions that are confirmed in less time than it takes to use a credit card.

The Bitcoin Blockchain is limited compared to competitors which have things like Decentralized Exchanges built on them which solves a lot of the Gox, BitStamp etc. issues.

So Bitcoin could be replaced by a blockchain offering currency stable assets, with low inflation and fast confirmation times as well additional products and services like a decentralized trading exchange. In that event most of the problems crypto currently experiences would be solved imo.