Your old box is probably a bit underpowered in the graphics area; however, if you are content on playing it at a fairly low resolution, it may work. WoW isn't a graphics intensive game like modern FPS games tend to be; however, the GF2 is REALLY old. You might want to check the min specs for the game with a quick google search. I never really played on older hardware than a Radeon 9800 (and even that card is quite a few years old). It ran the game fine as long as you weren't pushing terrain distance all the way out or pushing high resolutions (I later upgraded to a 6800GT which ran it with most settings at max (except for terrain distance) at a min of 30 fps at 1920x1080. As I said, the game doesn't demand that much, my ~5 year old PC in my sig runs it well... but a GF2 might have problems. Internet connection is important to some extent... you really just want/need a solid broadband connection to enjoy the game. It doesn't need to be uber fast... but it should be reliable/solid.
2600 arena rating is VERY impressive. Out of the 10 million players in wow... there are probably only a handful that will ever see a rating of 2600. That number is on the VERY high end of the bell curve.
The game is very addictive to some, and less addictive to others. It's an MMORPG... so the more time you spend working on your character(s)... the better they will be. There are plenty of people who play only casually for a few hours a week. There are others who play the game like it's a second job. I've done both, and definitely had more fun when I put a lot of time in. However, there is no way I can do that with my current schedule (so I sold my original account). I would recommend that you try the game out via the demo which will give you like 2 weeks of play to level a character (to a max of 20 IIRC). You can DL it from the blizzard site. If you want to get a 2600 arena rating... you have A LOT of gaming in your future... there is a lot to learn about the mechanics of the game, what classes can do what (and how to counter it), etc... before you can even think about being competitive. It's not a hard game to learn... but there is a lot of stuff to know... and you really only learn some of it it by trying (so lots of practice). Super fast twitch reflexes (a la FPS) aren't needed (however, you can't be a slouch for PvP).
Edit:
Here is the WoW system requirements. The GF2 (32mb) card is the bottom of the barrel as far as what they recommend. Personally, as per my experience, I would want a little more horsepower graphically. The celery is probably fine (again it's been a while since I've looked at older hardware)... I'd say 1gb min ram (non vista) for an enjoyable experience (IMHO only).
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