Update: I went and talked to another nearby recruiter, who happened to be a nuke, to see if I could get a little more straight forward answer. He told me that taking the test before I sign papers was a yes, and a no. He said there were only two ways to take the test:
1. I take it at meps, after my physical, and it would be graded on sight and I would find out then if I would get accepted or not.
2. The person in charge of giving the test could drive out to my recruiting station and give the test to me.
Here are the problems with both:
1. I was told that I wouldn't have to sign any papers saying that I am joining the navy up until this point, but when I asked if I could just walk out then if I didn't pass the test, he said that that wasn't an option and I would have to pick a job because he wouldn't take me there unless he knew for sure I would join the navy whether I made it into the nuke program or not and I also couldn't just walk out because I would have "wasted two days of his time." I asked my recruiter if he could find out what jobs would be available to me if I didn't make nuke so that I could have a back up plan ready. He told me that he could but it wouldn't matter because I haven't passed my physical yet so he didn't want to get my hopes up with saying I could get a certain job but then not be able to because of my physical.
2. I was told the person in charge of giving the test wouldn't drive to my recruiting station to only give one person the test because it would be a waste of his time, I would need like 5 or 6 others who wanted to take it too. I found out that the person in charge of taking the test was located only about an hour away, so I told my recruiter that I would drive out to him to take the test if he felt that it would be a waste of time to drive to me to give me the test even though it is his job. I was then told that even if I drove to him he would not administer the test to me because I haven't passed my physical yet, so it would still be a waste of his time to give it to me because there is a chance I could not pass my physical.
Side note: I'm still very confident that I would pass the nuke test without a problem. I also do not believe that my physical would be a problem either. I'm not color blind and have 20 20 vision. I'm 6'5 and 195 pounds. I work out, run, and play basketball all the time. I doubt my blood pressure would be too high. I do not know everything else that goes into the physical but I'm not too worried. Even though I'm confident that I would pass these both, I am still trying to watch out for myself, so any advice would be welcomed with open arms.
Thanks,
iNuke