If you plug PS3 (let's say GT HD) on non-HD LCD TV through HDMI and use HDMI->DVI converter on LCD TV side - do you still get HD resolution?
LCD TV of course supports resolution up to 1280x768.
HDCP is only an issue for movies.. games don't care. But, since the PS3 can't play Blu-ray at 720p anyway... you're not really losing out on anything. Except Blu-ray. But without HDCP, you couldn't watch them anyway.
But yes, the cable will carry the digital signal just fine. 1280x720 would do ya.