What it really boils down to are standards.
VGA is a simple analog RGB connection that transmits video only.
DVI actually comes in three different flavors, digial, analog, and digital/analog. In some instances, a DVI output on a computer can be connected to a HDMI input on a screen, however this is not guarenteed.
To answer your question: Yes, DVI can work with HDMI. No, a VGA input is not really necessary.