Yes the fat fast can be endangering, but I have heard much more extream diets to make a weight requirment for basic or trianing. Starvation, liquids, purging, duretics, steam rooms and so on.

If it has to be the weight gone or nothing, then maybe try it. Like suggested get back to regular eating for energy before you actually enter basic though, and be prepared for some of the weight to come back once you are on base foods.