Here's the situation in 2020. The current Windows desktop version of Microsoft Outlook (2013 and 2018, depending on your company) won't display syntax-highlighted, "fenced" code blocks, but other than that, emails composed with Markdown Here look fine, including inline math.
The fenced code blocks will look like this:
My workaround for that has been to use a <pre> block with each line indented four spaces, and I have a snippet expander do that work for me, so it isn't a pain. Your mileage may vary. It's not optimal, but it will display properly in Outlook for Windows.
You shouldn't have any problem with any other version of Outlook; Mac, Outlook Web, and the mobile app on iOS would display syntax-highlighted fenced code blocks just fine, because they are using modern HTMl rendering engines under the hood. (Haven't tried Android, but let's assume.) It's Outlook for Windows (which apparently still uses Word's HTML renderer, even in the 2018 version) that's the lowest common denominator you have to account for.
Hope this helps.
—Kevin