Not necessarily. What you may see is a shift to the Tangle instead of the Blockchain
The biggest short term change I see in crypto from quantum computing is in the mining process and the biggest long term change I see is the underlying technology, (which also affects mining.)
Currently quantum computing is in its infancy and early examples like D Wave are not currently better than traditional computing. In a blockchain, blocks are mined by computers racing to solve extremely complex mathematical problems and earn the rewards. In theory, these problems can be solved much faster by quantum computers because qbits can exist in superpositions and are not confined by the traditional definite states (1 or 0.) This means quantum computers can mine bitcoins much faster than regular computers.
To add to what you have said.
Cryptocurrencies right now use the blockchain as the distributed ledger on which all transactions are recorded. Traditional computers find it very difficult to break crypto security, but quantum computers (for the reason explained above) would be able to crack the encryption used for private keys. This makes them vulnerable to quantum computer attacks. This is why blockchains will eventually become obsolete and will be replaced by The Tangle, a new platform for cryptocurrency, that eliminates mining. It is also quantum-resistant. The first example of this is IOTA.