Coconut Oil does help boost your metabolism which aids in weight loss and burns off calories.
So yes by adding some coconut oil to your coffee you can help your body speed up the metabolism and calories will be burned off.
You should also watch your calorie intake and exercise along with putting coconut oil in your coffee to speed up the weight loss.
I like to add some coconut oil to my coffee and when I was on a diet I did lose some weight by adding the coconut oil to the coffee.
The coconut oil also makes the coffee taste good too so it's a win, win.