You are correct
klandsiedel that it is not a huge deal driver for someone to take the HBS core. It is a supporting point so to speak.
Your primary are:
1. UG GPA
2. Test scores
3. Work experience/career
4. Achievements/etc
5. Story/Career goals
So HBS core would be a supporting point to your Story/Goals or potentially GPA to change the story if the GMAT did not do that. But by itself, since there are no qualifications and it is pay to play, AdCom knows, it is not a replacement for your GPA, though if you say "my UG gpa is not representative, look at my high GMAT and HBS core, then it is a formidable argument.
However, I would perhaps engage with HBS Core/Other options if you have a story beyond "my GPA is on the lower side, I need something". Hopefully you can get more value (as it is going ot be time and pain and money to attend classes/etc) so hopefully you can get more of a story, such as "I am planning to pursue a career in XYZ and I wanted to start taking classes to make sure I can stand up to the academic rigor as well as to pursue my passion and I can see that it really resonates with me and I have been able to get a 4.0 GPA" or maybe even stronger and you can say "In my role I need skills for XYZ, and I could see I was not very comfortable in this new space having no background in Finance. I am able to start making a difference at my company - I have started implementing the valuation models and all of my execs are very impressed. Also I am finding many ideas where I can grow during my MBA and for the Internship. I am really excited to do my MBA and take classes about IB/PE and join the investment club for hands-on experience." - basically showing a bit more thought process and strategic point that you are not waiting for your MBA but taking action. AdCom like action and initiative.
In terms of the HBS vs. Local options - I think that's a minor choice. If you do want to be a part of the school and one of those programs attracts you, and it is convenient, then I would pick one of the local options. It may give you a good sense of what the school vibe is and what their culture is like and it very well add a bit more value to admissions as you suggested, and not only because you went to Emory in the evening by the way, but because you will be able to talk more about Emory or you will run into folks, etc.... and because you will be one of them, so it will be, HOPEFULLY, harder for them to reject you
Hopefully this makes a bit of sense. Sorry for the long answer.
TLDR version: don't take just for the GPA; probably not worth it. There is more value and reasons to do it however, and can make your story more powerful if you can pull it off at this point in the season.