I would like to save the output of my image processing OpenGL shader program to an image file and also display the result on the screen. I know how to save the window framebuffer using glReadPixels(). However, the resolution of the screen is smaller than the dimensions of the image.
If I render to an FBO, do I need to call glDrawArrays() again after saving and unbinding the FBO to see the results on the screen? Or is it possible to tell the window framebuffer to render from the FBO without having to run the shader program a second time?
To save the rendered image in the RBO, you can read the pixels directly by setting which buffer OpenGL will read the pixels from by calling glReadBuffer. In your particular case, setting the read buffer to GL_COLOR_ATTACHMENT<i> should do the trick. See the glDrawBuffer man page for details.
In order to display the image in the FBO: yes, you will need to make an additional rendering pass to copy the FBO's image into the default frame buffer. You an either bind the FBO as a texture, and render geometry, as you suggest, to get the image on the screen, or, you may be able to use glBlitFramebuffer to simplify the copying and image filtering.