Yes....but at 12 and 17, they're not likely to care whether it's good for them or not and food likes/dislikes are becoming fairly well ingrained.
I have 2 girls and they're quite a bit younger (almost 8 and 9), but they have always loved fruit and veggies. I have more trouble getting enough protein into them than anything else. Not that they don't like their sweets and junk food as well. What I do with them is compromise...they get 1 treat a week (usually ice cream after school on Fridays) and I allow them 1 bag of regular cereal per month. The rest of the time, they eat like we do with some added starches such as wheat bread and some higher carb healthy foods like fruit, yogurt and milk.
Education is the best weapon. If kids want a type of food (especially at the ages of 12 and 17), they will find a way to get it. Even in 2nd grade, my girls manage to trade what's in their lunch for what other kids have, so eliminating the junk can be nearly impossible. They do, however, understand what is and isn't healthy food for their bodies and what can happen to their bodies if they give them too much junky food (get sick, less energy, not feeling good), so that type of behavior is tending to decrease.
I do like the idea of telling older kids "If you want it, use your own money to buy it". I plan to use that method with high-priced clothing items that I expect to start getting asked for in a few years.


Edited to add: I moved this to the LC Parents forum so that it will hopefully get some suggestions from other LC parents who are struggling with the same issue.