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.
This is true when the time comes when bitcoins price do drop down into the lowest possible price or to the floor then confidence on investing on crypto would really be mainly affected which would result on pulling out investments out of crypto as soon as they can. We would really already have the negative impressions or do lost our trust on that time.