If you go EDO, you WILL go get an M.S. Not optional. That career path bakes in a free Master's in Physics or Engineering.
There's nothing wrong with getting an online MBA if you are mainly interested in the professional development of better understanding how your industry management counterparts as a senior EDO think.
That said, I would say hold off on any MBA until much closer to a decision to leave or stay in the Navy. The MBA knowledge really isn't applicable until you're quite a bit more senior (you don't interact directly with industry management as a junior officer), and if you decide you want to leave the Navy, you're better off delaying the MBA until you're ready to leave, to maximize its networking benefits to get you your new job.
If, on the other hand, you wanted to stay in the Navy as an EDO, after completing your M.S. and finishing your first tour would be a good time to get an online MBA to get the professional development, if that's what you're going for.
Looking very long term, if you are concerned about post-full Navy career value of the MBA, then an Executive MBA is, IMO, best value. I worked with a Supply Corps O-6 who got his E-MBA through UVA.