The answer is no. They are indirectly proportional to each other and when one goes up other goes down and vice versa. Why such ambiguity!? Well, it's simple, when this is happening people are actually trading alts with bitcoin on mass scale leading to pumping of bitcoin and thus making it fat over the time. If there is problem with bitcoin then surely people will start to dump bitcoin and out the thing into favourite altcoin making it more fat. The whole thing works like that. :-)
That is if the people will not convert from bitcoin to fiat currency. Take for example during panic last time when China announce something like banning cryptocurrency.
People holding bitcoins convert it to fiat currency and those holding altcoins trade with bitcoins then convert it to fiat.
The result? bitcoins goes down together with altcoins.
But now bitcoins recovered as well as altcoins.