Any training can cause injuries. However, many people argue that a Crossfit workout can be more injury prone than others. I think this is mainly due to the fact that their workouts can have you doing things such as deadlifts for reps immediately after a 1 mile run. The fatigue from the run can wreck havoc on your DL form making you more likely to get injured.
I think as long as you know your limits and know how to maintain proper form injury really shouldn't be an issue. Crossfit won't get you big and jacked or freakishly strong but it will get you in pretty damn good shape. I live in your area and I know that there are a few Crossfit gyms on the west side of EP, Im not military so Im not sure about on base.