Yes. It is oftentimes considered the second car. You can go anywhere in Sun City in a cart but you must stay on streets with speed limits under 35 mph. You will see them at restaurants and mnt other places of business.
There are many neighborhoods in Arizona that use golf carts to get around town. The are great for a quick trip to the store or the recreation centers. Golf carts are licensed motorized vehicles and must fallow all the rules that cars do.
I am In Sun City on a regular basis and on Saturday, I saw a lot of golf carts scooting around. You will have to make sure that it is properly licensed. The busier roads have a lot of traffic and you would probably feel safer keeping it on the side streets.