If you eat around 1200 calories per day and burn around 900 calories a day will you lose weight?

Yes you will.1200 calories a day is quite a low diet, so also if you are a sedentary person you will lose weight anyway.

Be careful of doing such an extreme workout. Burning 900 calories a day is very healthy but your intake should be about/over 1500 calories a day.

The risks are that you might lose a lot of weight really fast and as soon as you eat some chocolate or you simply go over your low calorie daily intake you'll put all the weight back in no time.