No, there will be no difference in quality as HDMI uses the exact same digital signal as DVI.
Looks like you are correct. I just found this:
The good news is that despite their differences, a backward compatibility for video exists between HDMI and DVI. Because HDMI evolved from DVI, they are both identical when it comes to video. But remember, DVI can not support digital audio. A good example is an older DVI connection on the source and an HDMI connector to the display. In this case, all that is needed to see the video is an HDMI to DVI cable. However, a separate cable for audio is needed to carry the the digital audio so the sound can be heard.