A blockchain is just a ledger. You do not need a currency to go with that. It is a neat and clever way of securing the transaction history. But a transaction could be an entry in your medical notes rather than a record of a solved puzzle changing hands. It is secure because of the distributed ledger meaning you cannot go back and change all of them.
All these currencies are is a solved puzzle which is passed around as a token of worth. Each movement is recorded using the blockchain.
You can have a blockchain without the currency. But not the currency without the blockchain.