It's all scaled though, so no it wouldn't. A resolution of 1280*960 on a game might look sharper than the same game on 640*480, but everything will still be the same size on the monitor itself. Player models won't be any bigger or smaller, and neither will the level, so it won't really make the slightest bit of difference, other than affecting your framerate.
However, I do know a lot of people that intentionally use a fairly low resolution on many FPS games, purely for the fact that the HUD and crosshair aren't scalable, and therefore are larger and easier to see at lower resolutions.
I suppose you could make the argument that a larger monitor is beneficial though, since although you don't see anything extra, you do have a larger area to look at, and thus more chance of spotting something small. That said, you could also say that it doesn't help since you might not be able to focus on the whole screen at once.