I know that girls that battle anorexia or extreme dieting lose their periods. do they get it back?

Most do, not all: In order to get your periods back you must regain adequate weight. Exercise may interfere with return of menstruation, too, and (annoyingly) may need to be drastically limited during the recovery period, even after weight is adequate. Dieting is very bad for the hormones in nearly every setting. When periods do not return it is usually because of low weight&/or too much exercise.