Can. Altcoin can be independent and can set its own market situation without the existence of Bitcoin as long as Bitcoin can be destroyed. At the moment there is one altcoin that is slowly starting to be free from the influence of Bitcoin, namely Ethereum. Ethereum is the only coin that dominates the ICO, so the price of Ethereum depends on the ICO not on Bitcoin, it can be called Ethereum is the king of the ICO. But hopefully all Altcoins can be free from Bitcoin and become independent.