Is a 1500 calorie diet healthy and sustainable if vegetables, fruit, lean protein and in processed carbohydrates are consumed?

Weight and Activity. Yes that diet can certainly be sustained if it provides for the caloric expenditure of the individual on a daily basis. The mix of foods you choose is also very good. By "processed" i assume you mean complex carbohydrates. If you happen to be 350lbs and 6ft 4in then you are going to be rather hungry for quite some time.