medschoolhopeful,

I assume you mean taking the pre-med courses at a level that is not intended for someone majoring in that field? The general rule is that you need to take the courses at the level which someone majoring in that field would take. For example, you need to take the first year biology course for biology majors, the first year chemistry course for chemistry majors, etc.

I suppose it may be possible to find a medical school that would not require that level of courses, but even then, you'd be at a disadvantage when taking the MCAT. You can try contacting some medical schools and seeing if they would accept that level of coursework, and please share what answers you get.

Having a BS would likely be no further advantage over a BA degree. The most important issues (aside from meeting the pre-med required coursework) are grades and MCAT scores. Your major and level of degree add little. Perhaps if you had a PhD, you'd have an edge, particularly if you are looking to have a research career. A masters degree adds little, and a BS is probably at least as common amongst med school applicants as a BA degree would be.

I don't know much about Naturopthic Medical School, but if your plan is to becoming an allopathic doctor, it seems like getting an ND would be a lot of additional time and energy, and some of the material will be redundant (although I'm guessing the intensity of the coursework at an allopathic school will be markedly higher than in a naturopathic program).

While I don't have any empirical data, my guess is that having an ND or serving in the military will add little to your chances of getting accepted into medical school. The biggest advantage to getting into medical school is to have a good GPA and good MCAT scores.