Are you planning to work as a paramedic? Excelsior's site states it is for "experienced healthcare professionals". It also mentions military corpsman as a possibility, so why not try for a MOS change if you are set in going in this direction. You could get the military to train you as a corpsman and get some healthcare experience.
I understand that you feel this is the only option you have, but please understand that this program is not going to set you up for success. Did you look at their CPNE (this is how they pass students on "clinical skills") pass rates? It was only 51.8% for those that finished in the 2013-2014 school year. The year before that, it was only 47%. That means after doing the whole program, only about half actually graduate and become eligible to take the NCLEX! And remember, this is from students that are "experienced healthcare professionals".
Reading their program information, they state that this program only for sure sets you up to be able to take the NCLEX in New York. Other states have additional requirements you will need to meet (many of which are clinical hours) in order to get a license in those states, so you may be limited in which states you can get a license/job.
In addition, while you are planning to then go into a RN-BSN program, you should start looking at what RN-BSN programs will accept your ADN from Excelsior. You have other options, even if they don't get you started right now. Also, you mentioned having completed your pre-reqs already, that's great, but many programs (RN-BSN) require them to be completed within a certain timeframe prior to your entry into the program. If they are more than 5-10 years old (depending on the program), you may have to retake those classes. Just something to think about.
Also, as you are also hoping to direct commission into the military as a BSN RN, please understand what the competition is for those positions. Right now, the competition is fierce for RNs looking to direct commission, it may get a lot worse (or better) in 6 years when your current commitment is up.
I understand you are already speaking with a recruiter, and that's good, but please think about what you will do if you don't get to direct commission into the military as soon as you get your BSN. If you truly want to be a nurse, there are better ways to go about becoming on.