I would have preferred it if you limit the scope of this topic to cryptocurrency and not the entire digital currency as Bitcoin can't take the place of many digital currencies it met to the point of becoming dependent on it. But for cryptocurrencies, I doubt if any of them would still survive if Bitcoin fails.
While there would be a crash, with the current state of other major cryptocurrencies like Ethereum, they can definitely withstand a Bitcoin failure. Smart contract platforms has simply found their niche already; with stablecoin transfers alone being a huge use-case.