Unless I miss something, it's very much not a standard measure of inflation. That said, leaning on that "at all": If wages are stickier than expenses, then the gap between wages and expenses will represent recent inflation to some degree.
If inflation is stable (and low-ish), then stickiness doesn't matter.
Sticky prices are only important, when expectations are invalidated.
So to fix your sentence:
> If wages are stickier than expenses, then the gap between wages and expenses will represent recent unexpected inflation to some degree.