In looking for a similar solution, I noticed that GMail allows it if you're copying and pasting from a browser.
If you copy from Word it seems to know the dimensions of the image (you can see an outline of the image) but it doesn't actually paste/upload the image.
From non-Office desktop apps there appears to be no support.
So on the assumption that Google engineers have dedicated some serious time to this, I suspect that it's not do-able from desktop apps yet but maybe if you could find a quick way to save the content to the web (e.g. using Word's blog or Save as HTML features) you could then copy and paste from that, if your client is prepared to take that extra step and you're able to let them save directly to a web server.
Nick
