I had this question a few months ago and was told that an adapter would not result in a loss of picture quality.
However, I was never given a technical response and as a result, am not completely satisfied with that answer. In fact, I kinda hope someone else chimes in on this thread with a more insightful answer.
I will say this though, one of the major differences between HDMI and DVI is that HDMI cables can carry both sound and video over, while DVI is limited to only video. As a result, one of the advanatges of a native HDMI port coupled with a graphics card with onboard sound, AKA ATI's HD 4000 series, is that its allows its user to experience sound and video with less cable work.