Hi Amy,
I think your plan sounds reasonable, yes.... you can't bank on schools to consider a score past the deadline, but at least you are showing that you are working hard towards improvement so that is a small plus over just leaving it as-is. You may also want to address how/why you feel you are capable of more and can handle the academic rigor of b-school, briefly. Here are some more optional essay tips:
https://www.mbamission.com/blog/2012/03/ ... al-essays/Some of the potential outcomes depend on what school/s you are applying to and the rest of your application though, keep that in mind. Ideally you'd have strong undergrad grades and evidence of quantitative ability elsewhere in your profile. And of course the overall admissions decision is based on your profile and application as a whole, so everything is given strong consideration-- your work experience, leadership, ability to make an impact, community involvement, specific career plans, demonstration of interest in a given school, recommendations, etc. Good luck!