Bitcoins value does indeed affect the price of all altcoins since BTC/AltCoin trading pairs are the most commonly used and is usually the standard go to exchange pair on all cryptocurrency exchanges. So can Altcoin break all the relationship from bitcoin and run as a independent currency.
I think it is possible but it will be difficult to remember so many bitcoin effects on altcoin so from that I tend to think that it is still very long realized unless bitcoin is no longer desirable or possible when there is a coin capable of replacing bitcoin then it can happen