Yes, MFP already puts you at a deficit to lose. If you don't eat back your exercise calories you are attempting to run your body on too little fuel.

For example, MFP tells you that to run your body and keep your normal weight you need 1600 calories so to lose 2 lbs per week (most you should ever try) you need 1400 calories a day (these numbers are made up btw, don't go by them).
You take in 1400 calories of food but you burn 600 calories during exercise. Basically if you don't eat back the 600 calories you are trying to run your body functions on 800 calories a day. Your metabolism will slow because your body thinks you are starving and you will not only be unhealthy because of too little food intake, it will actually be harder for you to lose weight.

I know it sounds counterintuitive to eat more to lose weight but it's true. There are groups on here, particuarly women who lift, who lose weight when they take in more food because they weren't eating enough. I upped my calories to 1800 a day and eat back my exercise calories and will eventually work my way up to 2200 because I'm trying to burn fat and keep my lean muscle mass. If you want more info, find the 2000+ calorie group.

Hope this helps.