If you get injured during BCT, it depends on the extent of the injury and the number of days that are left in BCT and how much you can participate with the injury. If it happens early on, you will be medically turned back, you will be able to return the following year provided you have healed from said injury. If it occurs towards the end of BCT and can participate some, they may let you stay. They have the final say. Either way if you start BCT and are injured to the point that you can't participate and are medically turned back, you should be able to come back the following year. Every year there are medical turn backs.
If you have a hernia that recently happened you should contact DoDMERB. It may be a DQ, but if the Academy finds out during In processing they will probably turn you away any how, you will have wasted a trip to Colorado and an appointment that could go to someone who is not injured right now. I could be off, but not by much I don't think.