OD tensile stresses would develop under the stated conditions. The magnitude of the OD surface stress should usually be negligible. As a rough guide if the depth of the induced compressively stressed layer is a tenth of the wall thickness then the OD tensile stress would be about a tenth of the ID compressive stress. With a ratio of a hundredth then the tensile stress would be about a hundredth. This follows from having to have a balance of the longitudinal tensile and compressive forces.Hence, high-intensity peening is not recommended for very thin sections - as well as because of possible distortion problems. If induced OD tensile stress is a problem then the outside of the barrel should also be peened.
