From a previous post:
"For modern autoflight systems, as on the B777, with filtered path definition, even if some type of transient LOC multipath interference should occur (e.g., with no LVP in place, or failed LVPs), and even if at low speed, that magnitude of apparent lateral displacement would not typically be expected. We'll likely just need to wait for the incident review findings to learn more about this one. ...as we continue to hope for early and widespread implemmentation of GLS, where multipath and related LVPs are largely irrelevant."
That means the airplane is essentially buffered against wild swings back and forth.
But let's not let that bother anybody - let the games begin.
Of course, if no one is doing what they are trained to do, like watching, then the game is anyone's call.