It will be some how difficult for most altcoins to survive as Bitcoin happen to be the market mover in recent time although at some point ethereum use to go against Bitcoin direction to the opposite trend which means some altcoins will survive the absence of Bitcoin.
that is in fact we have to accept that fact that most of the crypto currencies are depending on bitcoin, and if the bitcoin price will drop then it will really effect the whole market, in fact people interest on crypto currencies will decrease and which will really effect the whole market.