That's certainly possible. But, if the Fed sees inflation turn around without the labor market loosening up, they might take that as a win and lessen the rate hikes. Take a more cautious and slower approach than they've been projecting.
If they need to ruin the labor market to bring down inflation I think they will, but I don't think they'll go that far if it's unnecessary. That would just blow us right past a recession and into a depression, and I don't think Powell wants that at all.
Either way we'll see how this plays out, but this is some nice positive news either way for a change.