When detailed correctly at penetrations and transitions, stucco can function as an effective exterior air barrier. But as a face-sealed cladding system, proper detailing for water management is critical. Keep in mind that there are three types of stucco — traditional 3-coat, proprietary 1-coat, and drainable exterior insulating and finishing systems (EIFS) — and details can vary with each.
In general, exterior above-grade walls should have continuous air, water, and thermal barriers.
Installing rigid insulation as the exterior sheathing can accomplish all of these tasks, but you need to account for shear resistance (provide wall bracing) in other ways, and you must provide special details if you expect the foam sheathing to perform as a water-resistive barrier (WRB).
A double-stud wall insulated with dense-packed cellulose is an excellent thermal barrier; however, double-stud walls still need at least one additional air barrier to limit air leakage through the cellulose.
Check out the advanced framing section of Construction Detail Library for alternative techniques to achieve shear resistance, and check out Using Rigid Foam As a Water-Resistive Barrier for more information on walls without housewrap.
For more information on air barriers, see Questions and Answers About Air Barriers