The 8600gt (with the HDMI) should be able to. I used to have one but it did not have the HDMI output and I just had the DVi to HDMi but it did not utilize the sound at the same output and instead it went through the motherboard. If I were you, I would upgrade and at least invest in a GTX260 216sp. The one with an HDMI output so you can at least play 1080p and all HD formats at its best. Your games could then be played at 1920x1080, which is already full HD.
If you use the 8600gt, few games would be able to get past the 30FPS threshold for decent framerates in a game as the screen resolution or size would be too large to handle. You might end up getting a slideshow instead of playing the game. Imagine playing Crysis on medium with that card but the game would STILL stutter with probably 15FPS. Games like Crysis, FarCry2, Stalker2,GTA4,Gears of War, Batman, Dragon Age, World in conflict, Assasins Creed, Dirt,Grid, and some CODs would not run as well with the 8600, so contrary to what people are saying, I think you sohuld invest on the GTX260 or ATi 5770 with an HDMI.