Does the converter work?

Solution
A dvi connector has some pins that are analog, some that are digital, and some that are only used for "dual-link dvi" to allow higher resolutions. A dvi to vga adapter usually doesn't require all possible pins to be present. As long as it has all of the pins shown for "DVI-A" in this image, you'll be fine.
A dvi connector has some pins that are analog, some that are digital, and some that are only used for "dual-link dvi" to allow higher resolutions. A dvi to vga adapter usually doesn't require all possible pins to be present. As long as it has all of the pins shown for "DVI-A" in this image, you'll be fine.
 
Solution
It should fit on any graphics card with a dvi output. There are a few cases, like the Silverstone Raven 3, where a stub-style adapter will cause problems, but an adapter cable will fit fine. I'm a little curious what monitor you have that doesn't have dvi input, though.