The only issue you might run into is color space. DVI has a slightly smaller color space than HDMI, so with certain combinations of players and TV's you might run into black level clipping issues (it'll appear as black blocks during dark parts of movies).
I was using a DVI -> HDMI adapter with my tv, but it didn't work out.
I was using a DVI -> HDMI adapter with my tv, but it didn't work out.