At best anyone should expect to burn 5 to 15 calories per minute of exercise depending on your weight and intensity, on average I burn 10 cals a minute doing the stairmaster or walking which are moderately low intensity and probably 15 cals jump roping which is high intensity. The 10 minute work out looks to be a mixed of low and high intensity DVDs, low intensity being YOGA and high intensity being the cardio DVD. So I would say if she does Yoga, 50-70 calories, if she does the cardio at a good pace 110 calories. The answer is no, doing this alone isn't going to yield results without a change in her diet. Walking outside for 20 minutes a day would be less intense and help her more. If she stopped drinking regular soda, that would help her far more than 10 minute workout ever could. If she wants to lose weight with minimal effort, going on a diet and counting her calories would be all she would have to do.
This site talks about the 10 minute workout and what you can expect from it