I'm no expert, but this is my understanding --
The Canon S2-IS has been measured by DPreview.com as having shutter lag of approximately one/tenth of a second (The amount of time it takes from a full depression of the shutter release button (assuming you have already primed the camera with a half-press) to the image being taken.)
http://www.dpreview.com/reviews/canons2is/page4.asp
This can be longer if you have not already focused the camera with a half-press of the shutter. When you were shooting fireworks, if you pressed the shutter to focus on the sky rocket as it went up, you probably had a longer shutter lag of nearer to seven/tenths of a second. This "shutter lag" is ADDED to the amount of time that is required for a proper exposure of a particular image.
Obtaining good exposure for a photograph is achieved by allowing an appropriate amount of light to enter the camera and expose the film -- too much light and the photograph will be overexposed; too little, underexposed. The correct amount of light depends on your camera's settings ("film" speed -- ISO 100/200/400 etc., the aperture (yours was set at F8) and the shutter speed), the amount of light on the subject AND amount of light reflected into the camera lens. I found an exposure calculator on the internet that suggests that shooting fireworks at night with an aperture of F8, and a film speed setting of 400, would require a shutter speed of 2 seconds for a proper exposure. Your camera would have been calculating the proper exposure for you because it was set to the "fireworks" setting.
As far as ADDING another 1.3 stops by adding the polarizing filter, one stop difference is equal to TWICE the exposure time if the camera's settings are not changed, which would add more than 2 seconds to your exposure time in this instance. HOWEVER, you would NOT use a polarizing filter to shoot fireworks at night, but instead you would use it to reduce or eliminate reflections (shooting subjects behind glass) or reduce sunlit glare from lakes, etc. during the daytime. The polarizer would add to the length of time your camera would take to make a correct exposure, but this would probably be the difference between 1/500th of a second and 1/250th of a second (on a sunny day) -- then add on your shutter lag of 1/10 of a second, and you will see that the shutter lag will be more of a problem than will the polarizing filter -- if the subject is moving. If the subject is not moving, the length of exposure time is less important -- except for hand movement of the camera. You can use a tripod for slower exposures, or rely on the IS of your camera model for most exposures.
For more info on using polarizers, search google; you can start your reading here:
http://www.luminous-landscape.com/tu...larizers.shtml