If you're talking about a current-production Homelite, the answer is NO. Though you can get them to work properly, and occasionally one slips by quality control and is actually pretty reliable from the factory, in the end most of them are a pain in the behind. The refurbished 33cc units that you can find for $99.99 are a pain in the butt unless you know how to get and keep them running. I would not give these saws to a novice, where reliability is more important.
If I was buying a saw for a youngster, I'd aim for something that is simple, reliable, safe (think: no old saws w/o chainbrakes), and able to be serviced/supported. The latter point is reason enough not to get 'em a modern Homelite. Incidentally, I started with a little homlite XL-2 (26cc) when I was about that age. I got a lot of use out of that saw. I was schooled in proper, safe use, and never had a problem. By the time I was 14, my cutting was unsupervised and by 16 it was making me money.
Of the current crop of smaller saws, the Echo tail-handle saws would be my first choice. A CS-346, for example, is a good saw that will last a youngster for years, can be serviced (or parts had) almost anywhere that sells saws since almost every place I've ever seen saws sold sells small Echos, and in skilled hands can accomplish a lot of work. Plus, I have never seen a series of saw that can take as much abuse/neglect/ill-maintenance as these little Echos.