I'd jump into the debate on the merits of public health vs. direct physician contact but that the original question had to do with whether or not a public health department *internship* was a valuable experience.
You can't be a good physician unless you understand the system you're working in. This internship sounds great in terms of teaching you more about health care, especially if you're interested in primary care. Really though I think that in the end, do whatever the hell you want. You'll be tracked enough when medical school begins so why not experience something you're interested in, even if it's not related to medicine.
So if you feel like you'll learn, you'll enjoy yourself, and the experience sound rewarding, then that would be enough reason to go...