I don't think your condition will have an impact on whether you are appointed. I've had many candidates with known medical issues who receive their appointments once they have cleared the medical problem. However, if you are appointed, and your condition prevents you from participating in PS (this is determined by USNA Medical), then you won't be allowed to show up at I-Day or, if you don't tell them and you show up unable to participate, you'll be sent home.
First, check your DODMERB "paperwork." I'm almost certain that appointees are required to notify DODMERB of a change in medical status. I don't know whether applicants not yet appointed are also required to do so. If you are required to do so, obviously you should do so. If there is no such requirement, then you can wait to see what happens with your appointment.
I would not tell your BGO -- not b/c he/she is obligated to tell USNA but rather b/c we are told not to get involved in candidate's medical issues for privacy reasons. Thus, the situation really isn't relevant to your BGO -- it's between you and USNA/DODMERB.
If you are appointed, you do want to ensure DODMERB/USNA is told of your condition. My expectation is that some sort of "clearance" from your doctor will be required in order for you tlo be allowed to show up on I-Day. I would expect that, once at USNA, you will be examined by their medical staff to confirm you're good to go. If you meet those requirements, you're fine. If you do not, you would likely be sent home and told to reapply. Those "turned back" for medical reasons typically have little trouble being appointed the following year, if they have healed and they still desire to attend.
Bottom line is that the determining factor ultimately will be whether you are medically fit to be a plebe. That is a call for USNA Medical. Given the time between now and I-Day and, based on what you have said, that shouldn't be a problem. But I wouldn't try to "hide" the injury if you're appointed b/c if you do and they learn of it, you'll be in a world of hurt -- literally and figuratively.