Yes gaming mice can make a difference, they wont make you play any better, but when you are at the top of your game, that little difference in precision can make all the difference. buttons on the side can be quite convenient as well.
Zebra's right about muscle memory, even if you change the sens slightly on any mouse, it will throw you out for a while till you adjust.
There is also response time to take into consideration.. milliseconds in a game can make the difference between getting the kill or being killed, this is mostly determined by polling rate.
A standard mouse will normaly have a polling rate of 125hz and most gaming mice now run at between 500hz -1000hz, you can force polling rate on an old mouse, but if you run win7 it is a real bitch to configure.
The other and probably most important thing to consider is comfort.. for gaming you will be moving more frantic and more rapidly than when browsing or using other apps, so you need a good fit on your mouse, for example I tried out the razer naga, it was no good at all for my hands, it made me grip the mouse with my little finger and the mouse is pretty heavy, and arches quite high, so after a while of use it got really uncomfortable.
I use a deathadder now, its the biggest mouse I can find for my large hands, i run it at 3500 dpi and poll at 500hz, as i find 1000hz can get a bit skippy at times on my pc.