Depends on stubbornness of Core devs and if they are willing to redefine what Bitcoin is, namely, the miners hashing sha256 establish the longest chain consensus part of definition.
If Core devs have an agenda to win at any cost, they will create a different hashing algo client, I think LukeJr already did it with Keccak, and Bitcoin will fork into sha256 and Keccak two chains.
If Core devs give up, users will happily continue to use the chain that old good sha256 miners are hashing.
Do you have a different view?