Destroying Soul Society would involve the eradication of the Souls that live there and the murder of the 3000 or so Shinigami who reside within Seireitei.
If that happens, firstly Plus would go utterly unprotected and Hollows would multiply exponentially without Shinigami to keep them in check. Also, Plus would not be konsoed and so not come to Soul Society. In addition, with the Souls in Soul Society being destroyed, the circle of reincarnation would break down. So, literally, the world as we know it would be destroyed.
Some Hollow-fan/sympathisers believe this might be in some way beneficial to Hollows. However, there is no proof of this. The average low level Hollow is a being of negative emotions and thinks of nothing but destruction. Adjuchas menos and above are capable of complex thought but even they are ruled by instinct until they become Arrancar. However, whether they are Arrancar or not, Hollows in general represent an end as Hollows cannot return to the cicle of rebirth until they are cleansed by a Shinigami's Zanpakuto. So whichever way you look at it, the end of Soul Society also heralds the end of the Living World/Human World. Eventually, there would be nothing left but Hollows, who would turn on each other because they have nothing else to eat but each other etc, etc. So in short, it would be a regular doomsday scenario.