Using confocal microscopy we investigate the effect of attraction on the packing of polydisperse emulsions under gravity. We find that the distributions of neighbors, coordination number, and local packing fraction as a function of attraction are captured by recently proposed geometrical modeling and statistical mechanics approaches to granular matter. This extends the range of applicability of these tools to polydisperse, attractive jammed packings. Furthermore, the dependence of packing density and average coordination number on the strength of attraction provides the first experimental test of a phase diagram of athermal jammed particles. The success of these theoretical frameworks in describing a new class of systems gives support to the much-debated statistical physics of jammed matter.