No.
Basically, all graphics cards have a DVI-I output. These outputs support both Digital (DVI-D) and Analogue (VGA).
DVI-I - Digital and Analogue (VGA).
DVI-D - Digital Only.
DVI-A - Analogue only, basically the same as VGA.
That is why you can use a simple adaptor to change your DVI port on your GPU to VGA - it's not 'converting' anything, it's just using the analogue support, which is identical to VGA.
If you use a PROPER DVI-to-DVI cable to a DVI monitor, you will get a true digital DVI connection.
If you use a VGA cable with a DVI adaptor, it will ONLY output an analogue signal, and probably won't work on your DVI monitor (because they usually have Digital-only DVI-D ports). Even if it did work, it's still only an analogue connection, so you get none of the benefits of DVI.
There is no advantage to VGA, it's legacy, although it must be noted that DVI-D and VGA are both encoded as 8-bit RGBHV, so there's a whole debate right there.
Contrary to popular belief, HDMI is not the same as DVI, HDMI supports RGBHV all the way upto 48-bit (on the newest HDMI 1.3) as well as YCbCr (YUV).