Rwhalen,
I know this may be a day late and a dollar short for you, but the answer is "not likely". As a former BJJ practitioner and competitor myself, I had to put training on hold for years due to my TACP commitment. It is possible, but you will have little to no time during the training week, and you will likely be so physically beat down that its not a good idea. You would be unnecessarily putting yourself at an increased risk of injury, and thus, washing out, just so you can do BJJ. Wait until you finish, then train all you want.
-AV