Yes. I think your example illustrates the fragility of trying to use just one number to summarise the relationship between two waveforms. Consider a sine and a cosine (possibly derived in a physical system from the same source). The cross-correlation function is clearly periodic, but its average is zero. Even more difficult is the case where there is clearly oscillatory behaviour, but the periodic time is wandering, as happens in many common physical processes. This is clearly visible to the eye, but not to the single number. Even the cross-correlation function might blur the effect to relative invisibility.