I though this was a good idea so I looked into it. The only way I could see to do this cleanly was with a Plugin. This is my first attempt at a Plugin so use it at your own risk :) That said, I tried it out on my install and it works just fine. To try it, you will need to download the attached Plugin and make a small addition to the compose.htm templates.
To modify the template, add this code
Save message to sent folder: <input type="checkbox" name="plug_save_sent" value="1">
If you use it, please let me know how it works for you.