From what I know about the whole process, which isn't a lot mind you, first you send in all the paperwork for the MMD, along with your application, position acceptance for NCL and background check information. Secondly, they send you for a physical at one of the clinics located around the US and request that you send in a copy of your DMV record, Social Security Card, Drivers Liceanse, Criminal Background and Birth Certificate (Passport can take the place of BC and I believe DL). Once they receive your drug test results (which normally takes about 5-10 business days) and your other information then someone should get in touch with you about your background check.
I'm stuck waiting for my DMV record because in my state all requests have to be mailed into the state office instead of making it accessable at the local DMV offices, which is ridiculous considering I received my crimal background in 13 minutes.
I'm not 100% about the background check thing, I'm just going off of what someone else on this site said, which seems about right considering that NCL does everything one step at a time.
It makes sense that they would just have everyone go to the Regional Exam Center in Boston for their MMD after the week training at Piney Point. The only thing that's a little odd to me is that they would send you home after your training, especially since it can take so long for some Z-cards to come through. I would think/hope that they would start processing your MMD card a lot sooner, so after your training at Piney Point was over they would send you strait to the ship, but who knows. I've got to get in in touch with my recruiter once I get my DMV record and I've started writing out a list of questions I would like to have answered so I know what in the hell is going on.