Higher resolution will help in certain circumstances, though not so much with FPSs.
I can tell you right now, if you were playing Total Annihilation, RESOLUTION MATTERS. The reason is that you can simply see so much more on 1600x1200 versus 640x480 in that game. The guy running on 1600x1200 has quite an advantage.
There are some FPSs that it matters a little bit. A higher-res image of a player is more defined, therefore, you can see him just a little bit better. In UT, I find this helps because you can tell whether the dude you are seeing is a teammate or not sooner. Though the benifit is minimal after 800x600.
In tribes, if you were seeing "around" a hill, it would actually help to have a lower res, because the bigger pixels would actually give away someones presense behind a hill a second faster than at high res.
Then again, when you try to snipe at 320x200, things get inaccurate and very, very ugly /~unreal/ubb/html/wink.gif. There's a tradeoff for everything.
-Fringe