If a pre-existing injury or illness manifests itself during the first 56 days of training, you would most likely be discharged & invited to re-apply when you are fully recovered & fit to do so.
The problem with shin-splints is that you can take many months to recover and if you are medically evaluated as having a "new injury" they will, if realistic, attempt to rehabilitate you in Hunter Company. However, if it's looking like a long haul, you could still be medically discharged because you are not recovering within a realistic timescale.
Shin splints are the one injury that can be very difficult to realistically predict full recovery from. Conversely, a broken bone usually sets within a known period of time (unless there's complications) so doesn't always result in a rapid medical discharge unless it's a serious, complicated fracture.