Generalized Taylor-Aris dispersion (macrotransport) theory for spatially periodic media is used to study the dispersion of a point-sized particle during pressure-driven flow between two plates whose separation slowly varies in a spatially periodic manner.Invoking a lubrication approximation for the flow field, the macrotransport equations are solved in the long-wavelength asymptotic limit. Remarkably, the leading-order dispersivity during pressure-driven flow is identical to prior studies of electrophoretic and electroosmotic transport in such systems, provided that the O(1) Peclet number is defined in terms of the mean velocity of the particle. Particle velocity fluctuations induced by longitudinal variations in the mean velocity, rather than transverse diffusion in the local parabolic flow, are thus the dominant contribution to dispersion during this lubrication flow.