No, you don't lose weight from purging right away.
If you eat normal amounts of food and then just puke it up, yes, you will eventually lose a lot of weight.
However, if you binge and then purge, you really probably wont.
Plus, when your body isn't getting the calories it needs it goes into starvation mode so everything you do eat and actually digest your body will store. This also makes it harder to lose weight.
Bullimia will kill you eventually one way or another. Stop this in the beginning stages as it will be very very hard, if not impossible to stop later on.