Can you lay hardwood on concrete floor using mortar and grout?
No you can't do that. Even in Arizona. Wood has a high expansion and contraction ratio, they would work themselves out of the mortar in under three years in the driest of climates.

Your best option would be to membrane underneath the boards, secure them with concrete nails, and epoxy, or caulk the joints. That might last a year.

In terms of code, in the north it's not allowed. Untreated wood cannot bare directly on concrete.