Blockchain Technology was driven to fame by its application on Bitcoin Gold due to its encryption that has been considered hacker proof. Bitcoin has been used as a reference to its success, providing a secure network for users.
The question however is, can blockchain succeed without bitcoin?
BTC and blockchain were born at the same time. BTC blockchain was reserved only to carry out transactions and nothing else can be done over it. It was ethereum who gave the concept that blockchain can be used for other purposes as well. Today there isn't even a single business that  can't be migrated to the blockchain.
If we see blockchain from BTC prospects, we can say with confidence that there is no future of blockchain without cryptocurrency. 
But with so many DAPPs now running over blockchain (thanks to ethereum), we can say blockchain can survive without cryptocurrency. 
In fact, cryptocurrency is just one application that is running over blockchain, blockchain technology has prospects that are yet to be discovered by the human mind.