The short answer is that yes, it will do that. It will take some tweaking and refining however. The calories eaten side is going to take a lot of practice to get that hang of without breaking out measuring cups, spoons and scales every time you eat something. After a while you will get the hang of it, and nutrition labels are great at coaching you along too in determining how large a portion of something is. The calories expended side is a little more iffy. Everybody's metabolism varies from the curves used by the software, since those are curve fits of "typical" metabolisms. By varying your activity level to account for where you are plus tweaking which method the site uses, you should be able to get very accurate measurements over a several month period.
I have essentially tracked everything I've eaten since 1/1/2011 (a few days missed here and there) and all my major exercise activities (including yard work as well as actual workouts). I had years of experience doing this during diet/fitness periods but never as just a daily journaling. I also measure my calories expended during activities with a heart rate monitor for more accuracy (sometimes FitDay nails it other times it is off by a lot). After a few months I found out I was way over-estimating my base calorie expenditure level (an error of 2 lbs over three months in the very beginning). Adjusting for that I have been able to track my weight change over a period of more than a year to within 0.5-1 pound. That is with targeting a net fat loss of as little as zero pounds and as many as 2 pounds every three months.
So again, short answer is yes it works. It will just take some practice and tweaking.