It is not necessary for a candidate to have a nomination or an approved DODMERB exam to receive an LOA. My understanding is that an LOA requires the candidate's application to be completed and a passing PFA.
LOAs are given earlier in process and are often conditional upon successfully completing DODMERB, a nomination, 7th semester grades, etc. At least that is how it worked for my DS. His LOA came in early Nov '13, his nom in early Jan '14 and his DODMERB approval in Feb '14 (late as I recall). Both were conditional in the LOA as well as his seven semester grades.
I suspect if medical and nom were good to go, USMMA would simply offer an appointment, conditional the on 7th semester grades.
BH
PS. I highly recommend a visit. I believe it is viewed very positively by the admissions staff. Nothing to back that up other than my subjective opinion.