>2550x1600
Assuming you mean "2560x1600", yes, both the 8800GTX and R600 will output this resolution. They all have dual-link DVI ports.
As for 1080p, no, neither will drive it as 1080p - it will have to be upscaled to fit on the display - whether by the monitor or the card. I suppose you could force it to display on a 1:1 pixel map, but you'd be wasting approximately a third of the screen on black space.
I would imagine that 1080p video would look *amazing* on the 3007 monitor - it won't be any worse than a true 1080p screen (and will probably be significantly better) - but it won't be displaying in native 1080p. In exactly the same way as a 1080p screen won't display native 720p - it upscales.
As far as I am aware the 8800GTX has full support for HDCP.