The resulting image quality depends a lot on the quality of the D2A conversion (typically called a RAMDAC) in your video card. Of course you can lose a bit in the A2D if you're plugging in a flat panel, but it probably will just be a slight reduction in clarity
I haven't seen any really bad VGA output in a number of years, however 10 years ago the results were often terrible. Companies would concentrate on being the 'fastest' card and the resulting image quality would be terrible - like setup a good monitor and aim for the highest resolution and refresh rates and you couldn't read text on the screen. Install a Matrox card and the image would be absolutely crisp.
On the D2A side, your image is a bunch of numbers - sharp lines are indicative of numbers that differ by quite a bit. So black text on a white page will be a very sudden transition between 0,0,0 and 255,255,255 (RGB values) and back again. Now try to convert this to analog - if the DAC and associated circuitry isn't well designed, you will end up not quite getting up to 255, 255, 255 on the pixel you want it at, and then not getting quite back to 0,0,0 for a few more. The result is a few more shades of gray rather then the crisp black and white you were looking for.