@Sholom's comment regarding pandoc-crossref
inspired me to have a read, I was not previously aware of it and it is not available as an extension to rmarkdown
currently.
It is entirely possible to achieve basic equation numbering with this "filter".
Markdown
---
output:
word_document:
pandoc_args: ["-Fpandoc-crossref"]
---
$$a^2 + b^2 = c^2$$ {#eq:eqn1}
$$\log xy = \log x + \log y$$ {#eq:eqn2}
$$\frac{df}{dt} = \lim_{h\to0}\frac{f(t+h)-f(t)}{h}$$ {#eq:eqn3}
Output

pandoc-crossref
The binary releases of the code are located here. From a windows machine, I dropped the pandoc-crossref.exe
into my Pandoc install folder alongside pandoc.exe
and that was sufficient to allow my markdown to render.
N.B. I did this with a standalone install of Pandoc, if you are using the version bundled with RStudio you may need to install differently.