Yes, there is phase delay between them. The amount of spacing and the amount of phase delay determines the directional pattern - just like phased verticals, dipoles or any other element.
The amount of phase delay varies with frequency. But so does the spacing with respect to wavelenth, so the delay tracks over frequency for several bands (depends on the spacing/offset between the elements).
So you don't use any phase delay between them? I wonder what is the point of staggered layout? Lankford uses a delay based on angle of signal and distance between antennas.