You can definitely lose weight eating this way. Losing weight is typically the goal of people when they make a diet change. This is a noble pursuit and a great idea in general. What makes this way of eating unique is that it has results that sustain and it causes tremendously positive changes in overall health. That, in the end, should be the goal. If you don't feel great and are on maintenance drugs, your goal should be to get off all those drugs and feel better than ever.
Here is another great example of the results of this diet from Marks Daily Apple:
Within a month of ceasing my refined flour and sugar consumption and adopting the Primal Blueprint, I began to see immediate and dramatic results. My lifelong symptoms of severe asthma immediately disappeared, my painful gastric reflux abated, I dropped 15 pounds that first month, and I was able to cease all prescription medication almost immediately.
Now, 11 months after beginning my weight loss journey, and 8 months after going “Primal” I see dramatic results. My weight has dropped about 105 pounds to 220, with my average monthly weight loss being between 8 and 12 pounds consistently.
New Years resolution time is coming. Rather than just eat less like typical diets call for, why not make a real change that actually works?