If Comet Ison were to break up passing close to the Sun, Would the pieces of the comet emerging from around the Sun, Could those various size pieces somehow Shotgun the Solar System?
The tidal break-up of a comet is, in astronomical terms, a comparatively 'gentle' event and the various fragments of the comet would continue on very similar orbits. The comet Shoemaker-Levy 9 that impacted Jupiter in 1994 is a very good example. When it collided with Jupiter in July 1994 it did so as a string of at least 21 fragments as a result of having been tidally disrupted during a previous close passage of Jupiter 2 years earlier. After the tidal disruption event all of the fragments retained nearly the same orbit such that they all collided with Jupiter over the course of 6 days in July 1994. More directly similar to the comet C/2012 S1 (ISON) is the Kreutz family of sungrazing comets, which are all believed to have originated from a single large comet that fragmented during a close passage of the Sun.
As a side note, the correct designation of 'comet ISON' is C/2012 S1, the (ISON) appended after the designation just indicates the organisation that discovered it, in this case the International Scientific Optical Network, based in Russia. It might seem somewhat pedantic, but the ISON team will discover other comets (it is what they do), so there will be other comets with the suffix (ISON).