Does having strong legs, calves and hamstrings stop you from injuring your achilles, ankles and from getting shin splints?

Sorry, no.: Getting shin splints is usually a pathomechanical pathology ( things aren't working correctly). Strength is only one factor in allowing for normal mechanics, along with range of motion, an array or joint interactions and forces acting through these joints, as well as anatomic considerations. In fact, over strengthening one muscle group to the detriment of another may actually cause problems.