I have the 9600 GT and it runs smoothly for the most part. Everything at max besides the view distance settings. I left those at default. Only time you might notice some slowdown is when you're in an area with a bunch of people, but that isn't very often. Only time I got that was at the beginning when you beam down to a planet and fight some borg. After that... most things are on a smaller scale of battles.
Yes Star Trek Online can run on a Nivida or ATI video card with 512 memory. You may have to use the video card software to do some tweaks to get high end rez. The only problem you may encuonter at this time is lag issues in some areas of the game.
Just a note: Do not blame all lag issues on your video card as a lot of users have reported lag issues that have high end systems. Remember this is still Beta.