I just tested this out and can confirm that you can submit markdown via the API to be the body of an issue. The whitespace will need to be encoded as special characters, but everything else should be the same as you would expect.
If you'd like to see this in action, I would recommend using the Get an Issue API endpoint to pull down an issue full of markdown formatting so that you can examine the formatting. You can even copy the body from that issue into a new issue created by API.
Hope that helps!