No, Fraps can't be used for desktop recording, because there is no DirectX or OpenGl activity. You can record only launched applications and games (99 % of the cases) that were developed using DirectX and OpenGl. You should see if Fraps is activated by the presence of FPS display in one of the four corners of your monitor.
To have a desktop solution, choose an application like Camtasia. With Camtasia you can record every activity on your desktop, regardless if it's full screen or not, game or an application.