Is it possible to directly embed an image into a Markdown document?

Yes, it is possible, using data: URIs and base64. Terribly inefficient though:

![Hello World](data:image/png;base64,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)

Unfortunately Super User does not allow data: URIs, it would look like this:

Whether this will work of course depends on whatever you’re using to (pre)view the document. It has to support and allow data: URIs.

I did some tests and embedding usually works with online markdown editors like dillinger.io, jbt.github.io, stackedit.io, so this topic isn't so black and white as @Spiff wrote above.

This is a screenshot of two base64 blocks inserted by using 1) an internal reference and 2) a common image insertion (see the code below).

1) the referenced base64 block stops being parsed right at the point where 'a new chunk of image' starts, the green part ... So4Z4wxkXa7KukmKul2dDvd ...
2) by passing the block directly we get the whole image

code

1\)![png tester1][pngtester1] 2\)![png tester2](data:image/png;base64,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)

_1\) the referenced base64 block stops being parsed right at the point where 'a new chunk of image' starts, the green part `... So4Z4wxkXa7KukmKul2dDvd ...`  
2\) by passing the block directly we get the whole image_

This was tested with http://tmpvar.com/markdown.html. I don't know how it behaves on github. [The issue](https://github.com/github/markup/issues/270) has been already well discussed.

[pngtester1]:data:image/png;base64,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

This was tested with http://tmpvar.com/markdown.html. I don't know how it behaves on github. The issue has been already well discussed.