Vinca minor (periwinkle) requires partial shade and moist soil conditions to thrive. You might be able to provide the irrigation but the full sun would probably scorch the leaves and make it look shabby.

I would suggest that you contact your cooperative extension office for a list of recommended groudcovers for your area. Or a "good" nursery should be able to give suggestions. Just remember that nurseries are in the business to sell you plants so some might sell plants that are not the best choice for your location.

I'd avoid the vinca - it's just not going to perform well in your situation and it's pretty ineffective for any kind of erosion control. I'd look at things like creeping/prostrate rosemary, Cotoneaster dammeri, Arctostaphylos, Pt. Reyes ceanothus or even groundcover junipers. All are extremely drought tolerant once established, do not need excessive irrigation to become established, will thrive in a hot sunny location and are woody-based, providing greater erosion control.