What a paradox!
They are asking participants to break the Bitcoin cryptography then they want to pay them in bitcoin which would become worthless if they succeed

If there'll be any successful attempt in the near future, it would take a lot of time on that single attempt.
Given that, there'll be enough time for announcements and soft/hard-fork to issue a QC resistant update.
Lots of "
satoshi" bitcoins will eventually be redistributed to the market that will drop Bitcoin's market value together with FUD,
But I doubt Bitcoin will be worthless if an update is successfully deployed in time.