In high school athletes things like shin splints and other over-use injuries are quite common. I have found these injuries occur for a couple of reasons:
1. The student-athlete is new to running or have running back ground.
2. Not having the proper shoes.
3. Improper training such as the increase in mileage to sudden (i.e. they did not run all summer then try to jump into training with their friends who have when the season starts.
4. Running on concrete
One thing we have done and have seen a dramatic decrease in injuries is quite simple, run on trails. I realize this is more difficult for some teams more than others. Despite having a small team of 40 or so and being at a prominent football school the administration has been supportive in getting us vans and buses to travel to trails for training. This means much of our time that might be used on form drills and strength work, etc. is used on a 20-30 minute bus ride but for us staying injury free and getting in 8-10 miles on trails has increased the enjoyment of running and reduced injuries. It give the kids social time on the bus and is more fun than running on smog filled congested streets. It also keeps them moving as they don't have to stop at lights.
Some other things we do to curb injuries:
1. Instead of a morning run 3 times a week on the roads we do an hour pool running workout.
2. Instead of using our track we run down to the local Junior High and use their dirt track and grass field.
3. Ice bath after every hard workout.
4. Do the little things to strengthen your feet and shins.
This is all mostly applicable for cross country but I write this because we have begun to transition our distance team in track to be more like XC. We start with a month or two of base running like we do in the summer introducing fartleks, tempos and strides. We hold off on the hard VO2 Max work until later in the season (January to June is a long season, especially following XC from June-early December). We don't start hitting the track until March, which in California still gives us 3 months of hard track training.
But to answer your question is it possible? Yes. Optimal, probably not. But following our XC season we always do a mile time trial. And every year we have 70-80% get their personal best. I think for High School athletes the biggest factor is aerobic training, gaining strength from mileage and physical development from maturation.
Is it possible? Absolutely. Model the start of your season like a cross country season and then go from there.