Mac Mini Display output

No won't work:

The DVI to Component Adapter gets the signal out of the four analog pins:

but the DVI/HDMI Output from the Mac mini didn't have the 4 analog pins. The signal is full digital.

Also have a look here:

Can the HDMI port drive analog displays (VGA displays for example) using adapters?

No. The HDMI port will drive digital connections—such as DVI—using the adapter that came with the Mac mini, but cannot be used for analog displays such as VGA. You can purchase a Mini DisplayPort to VGA adapter separately to drive analog displays.

To do so, you need a video converter like these from Atlona.

What is the video output quality of the Mini DisplayPort to VGA adapter? My analog tv has a large HDMI capable port (i have an adapter) but the fonts are too small and are all fuzzy on the screen. Odd since my direct TV connected right to it fine.

Does the mac min have to have a real digital TV in order to work correctly?