For ref, I totally wrote off my back during basic, but spent 5 months on PAT platoon doing daily physio/rehab before recoursing and getting it done. I couldn't move my arms/torso enough to dress myself for a while, let alone do anything useful, so was definitely a course ending injury, but lots of people had minor things with restrictions that didn't stop them finishing, so really depends on the nature of the injury and when it happens in the course (ie big difference to miss the field portion vice a few days of garrison classes).
If you talk to your instructors that will help, but worse case there are lots of processes in place for folks that get injured to heal up and get back in the saddle.
As an aside, you may want to also look at how you are running. I used to have crippling shin splints, but switched to running on the pad of my feet (aka Chi running, and other names). It takes a while to build up to it, but it completely changes which muscles are engaging and massively reduces the shock load (by letting the natural mechanics of your feet and legs act as shock absorbers). For me that pretty much eliminated the shin splints. The minimalist shoes help with learning that as there is no real padding on the sole to take up the shock, so it actually hurts if you land heel first.