From my own experience, I could not tell you about the progressive scan method of connecting to a monitor.

The truth is that the VGA box worsens the video quality when using a computer monitor, because of the nature of the source video. Whereas (supposedly) using the progressive scan mode (with the appropriate modified cable) of the GameCube will get you better quality video on a monitor. But then, if you have a TV that uses component video, you could also have that same quality. It's not necessary to connect to a computer monitor. The reason I want to is because we don't have TV's at work, and the weekend 3-11 can get quite boring.

The connection/video quality issue is explained in more detail in that other thread I linked to, if you find my summary somewhat lacking.

Edit: Keep in mind that the progressive scan connection method will not work for games that are not progressive scan capable. Currently, I only have Metroid Prime, which is.