Ridiculous is to give away a 5 year visa for a dentist appointment or a two week cooking class without even to prove how people can afford to live here. Especially if you are calling for "quality tourists" all the time. But okay... let's use the options as long as they exist... we all know how fast things can change here...
You don't need any kind of visa to buy a vehicle. But if you want to register it in your name you need a "certificate of residence" from the Immigration. And to get this you need to do a 90 day report first (officially). Since you can stay longer than 90 consecutive days with a DTV the answer is yes, you can. If your local Immigration has different requirements and you face any problems you can use an agent as well.