Should I fertilize my shrubs?

In general, fertilizer is not necessary in our climate.  If you have shrubs that are desert adapted and suitable for our area, then they will thrive in our arid climate and alkaline soil.  Your larger concern is planting them correctly, in the correct location, and irrigating them correctly.

Beware of the pretty, tropical shrubs that attract so much attention at the big box stores.  They are fresh off the delivery truck, have been grown in an artificial nursery environment, and are raised in a humid environment with the intention of preparing them for a quick sale.  While beautiful, these shrubs do not have the genetic adaptations that are necessary to survive our heat and soils.