People have thought about this, and it is possible in theory, as follows.
In Moodle 2.3, you have you upload new files using the File picker, and repository plugins. As well as the standard plugins like 'Upload a file' and 'My private files' etc, it is conceivable that someone could creat a new 'simple sketch' plugin, where instead of uploading a file, the user can draw with their mouse right there in the file-picker window.
Unfortunately, no-one has made that plugin yet. Arout the Moodle 1.9 time, we had a GSOC student, Mihai Sucan, who made a nice JavaScript sketching thing called PaintWeb (http://code.google.com/p/paintweb/ ) The theory was that once the Moodle 2.0 repository system was finished, PaintWeb would be made into a repository plugin. However, Moodle 2.0 took longer than expected, so that never happened. (I think Mihai got a job working on Firefox.)
Anyway, it could still be done, and if it was, then you could use a sketch anywhere in Moodle where you can upload a file (e.g. in a forum post). That would be very cool.
Similarly, people have tried to do 'record audio' or 'take a screen-grab' plugins. Have a look in the plugins DB.