Here's the thing.
With HBS (as with any other top b-school, but moreso with HBS), there's a TON of super accomplished and/or super blue chip people applying - and some have incredibly compelling backstories and narratives. However, it really comes down to numbers - there's only so many seats and as such just because you are super accomplished doesn't mean you will get in.
In plain English, you have the elements of a compelling application that an HBS adcom will take seriously, but you really do have to be prepared for the possibility that you still may not get in. The truth is, while adcoms like to publicly tout how they love diversity, they want compelling people, blah blah blah and how they want non-traditional, unique applicants -- at HBS in particular they tend to go with the safer choices in taking your standard issue Ivy types -- those who did well academically at an Ivy or equivalent (i.e. it's not just about pedigree of school, but getting strong GPAs on top of that), and then spent a few years at a top tier firm and/or in well known avenues such as Teach For America, Peace Corps, the foreign service, etc. That's their bread and butter. In a way, their bread and butter are those folks who experience a marginal benefit at best from the "Harvard" brand simply because their resumes are already full of pedigree.
Do they accept true "non-traditionals" (i.e. those without pedigree, but have had some unique experiences, achievements, etc.)? Absolutely, but it's more of a wild card. It's hard to predict. And this has little to do with the GMAT or GRE (take either one - HBS isn't really as hardcore about standardized tests as other schools).
Practically speaking, if you're really that gung ho to the point where you're HBS or bust, just be prepared for the fact that it could really go either way in your case.