I think '74 or '75 was the first year that a converter appeared on vehicles. So it won't be a requirement on your '72. It will however need to pass visual and dyno testing, required on '67 and later.
From the website:
http://www.adeq.state.az.us/environ/air/vei/tech.html
Steady State Loaded/Idle: This test is used for most 1967 through 1995 vehicles in Tucson and 1967 through 1980 models in Phoenix. The vehicle is tested at idle and (depending on vehicle class) at approximately 25 to 30 miles per hour. The results are shown in percent or parts per million.
Tampering: In addition to one of the above tests, a vehicle may undergo a visual inspection to determine the presence of certain emission control components as installed by the manufacturer. Inspection includes catalytic converter, operational air pump, positive crankcase ventilation system and evaporative control system. These inspections coupled with the evaporative system integrity (pressure) test constitute the tampering inspection.
Then there's this: Maybe an out clause for one time registration but you could never sell (in Phoenix)
http://www.adeq.state.az.us/environ/air/vei/fail.html
I think that a station will give you the requirements list. Its then up to you to make it pass. I wasn't even aware that you could transfer the title without testing.