If it's noticeable enough, yes. I put a screen protector on my PDA and iPod screens within 15 minutes of opening them, though. It's so gratifying when the screen protector gets so dirty you need to change it, that you peel it off...to find a factory-new mint-condition screen underneath, just like when you pulled it out of the box. "It's so shiny..."
I don't waste a screen protector on the phone though. It's a clamshell, so the important screen is on the inside (it has about 10 dead pixels sprinkled across the bottom from so much abuse). It's an LG VX6000, the thing is built like a frickin tank.