I think so. It does mean that you can be charged NI contributions on earnings above a certain limit, though. For the average fifteen-year-old with a Saturday job, this is academic, because you're unlikely to earn enough to qualify, but if you were to earn a decent amount of money, say, modelling, acting or singing, then you'd be charged at the going rate.
Saxyjag - it's not out of the goodness of the government's hearts. They are not giving out favours.
National Insurance entitles the payer to claim sickness benefits and other benefits. They don't want to be paying under 16s when they are off with chicken pox. :)