regarding sugar, there is no scientific basis for claiming that sugar is unhealthy.
regarding fat loss - it makes no difference how much sugar you eat as long as you are in calorie deficit, so yes you can loss fat while eating sugar.
Intake of sugars in relation to fatness and micronutrient adequacy.Bolton-Smith C.
Cardiovascular Epidemiology Unit, University of Dundee, Ninewells Hospital and Medical School, UK.
Dietary sugars have frequently been linked with excess body weight and poor quality diets. A review of the recent research in this area reveals no basis for a causative association between sugar intake and obesity. Rather, a diet which contains a high percentage of energy from carbohydrate (starch and sugars) may assist in weight loss if the proportion of energy from fat is low. Nutrient inadequacies tend to occur in susceptible groups (generally women and children) who have a low total energy intake, and this is compounded by a relatively high contribution from sugars. For general populations with an adequate caloric intake nutrient adequacy can be achieved across a wide range of dietary sugar (4-20% energy). In this respect, intakes at either extreme are sub-optimal.