The answer is yes, depending on what mouse you are using and the driver you have installed. If you have an intellimouse, download and install the newest drivers from Microsoft, this will allow you to have program spacific control on the buttons you want to customize. So far I haven't found a driver for any logitech mice that will support Solidworks, but I am still looking.
I bought a mouse a few weeks ago, and installed the latest Intellimouse software, but they took that 'program specific' function out of it. So i installed my old version 4.0 intellimouse so i could customize the buttons.