If you mean 'culinary' when using the term herb and not herbaceous plants which means: stems and leave dye and the new plant emerges from the root in the spring, then the answer is yes. Most are heat and drought tolerant but not very many I would classify as ground cover, less than 6 ins. high.

Rosemary grows well in heat with little water. Mine has grown into a hedge. I don't know of any herbs that would fit the ground cover definition. I have luck with basil and dill

I should have been more clear. I want to plant medicincal and culinary herbs in the ground as landscape accents with rocks. I'm curious what will do well in the ground and in full sun. I hoping the group here can help me come up with some plants that would work. I'm considering Echinacea, Thyme, Lovage, English Lavender, Oregano, Catnip. Any good ideas or plants that won't work will be appreciated. I also heard that Arizona has a variety of hot chilli pepper that grow wild. Anyone know what that is?

I'm look for perennials.

In the four corners area of CO we had several varieties of lavender that did well with only occasional supplemental watering. Also Catmint French Taragon and of course Russian Sage.
There are procumbent rosemarys and they are attractive and durable ( also safe from javelena and bunnies) but, rather slow growing.
I'll be watching this post as I have hopes of a similar project up towards Prescott.

rosemary does really well here, there's an upright form and trailing variety - both grow quick, the latter grows into a hedge if you let it.... both have the typical aromatic qualities one would expect from rosemary.