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.
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.