Betsy, I have been on several cruises where there has been a kids sail free promotion and have never noticed more than a handful of children on board. March is prime time spring break for the kids, maybe someone who has sailed during this time will pipe in as I don't think my cruises were in March but I can't be sure :)
As far as I can remember, we have only had one account of kids gone wild on a cruise and that was several years ago. Since then, I don't think I can remember anyone mentioning an invasion of young'uns on their sailing!