If they are wise, that is literally what they will do. It won't undo the fork, though, the fork is really in the blockchain (as he's using the term fork) rather than in the source code.
For some period of time there will be two versions of bitcoin running on the machines that mine, and it will take some time for them to switch over-- but since Classic is doing the switch with major support now, the transition should be smooth.
Bitcoin the protocol can and is run by a wide variety of software... the blockchain is a consensus agreement of that software. Basically its an agreement on protocol based on the rules in the software.
For most of its history, that software has been based on Bitcoin Core. That may change in the future to Bitcoin Classic, or both may be running at the same time with different variances, but supporting effectively the same protocol.
Nobody wants %50 of the network to be running software incompatible with the other %50.