It depends on what you mean by "unsupervised." 

My son has run a monthly game for years - he's 14. Most of his players are about his age, but some are younger. Mostly, the youngest come attached to older siblings, but that's not always the case.

Those kids are playing unsupervised in that their parents are not at my house - they're out shopping and going to lunch in places you can't bring kids and running errands and generally being giddy at the prospect of 4 hours of free time. 

But they're not unsupervised because at least one adult is at the house at all times.

So if by "unsupervised," you mean, "without an adult participating in the game," I think you can let them play as soon as they express the interest and have a GM and gaming environment you are comfortable with.