You probably will decrease shutter lag by manually focusing on infinity because that's one less thing the camera has to do. My Coolpix is pretty slow in the AF department, too. However, you could also hold the shutter down halfway to lock focus and then shoot (if that's an option).

If you lock the focus on infinity, then you will probably have quite a few out of focus images. Digicams have such short focal lengths (we're talking actual focal lengths, no 35mm equivalents) so they will be better at this than anything else out there. Stopped down to f8, you'll probably get most everything in good focus but it's not optimum - you may have a slow shutter speed for example.

Time for the term of the day: "Hyperfocal Focusing" If you google that term you'll find some charts where you put in the lens focal length (again, actual number), the aperture and the distance you focus the lens at. The chart will tell you how far in front of and behind that point is considered to be in focus (YMMV). You'll get 1/3 in front of that mark and 2/3 behind it. If you have any prime lenses - especially manual focus ones - they have these markings right on the lens barrel so no math is involved.

So the short answer is... maybe! ;) The trick would be to play around with the chart using the focal length and aperture you want (might as well choose the minimum available on the camera, for starters). Keep moving the focus point forward from infinity (or 50' would do) until you get "infinity" on the far end of the scale and the closest distance you can at the close end of the scale.