We spend lots of resources and time on social networking websites from all over the world. How we justify social networking sites are brings people, society together? Are there net gain or net loss?
(If I have understood your question properly) The major role of Social Networking sites in the sustainable living is:
Spreading awareness about the environmental problems that we are facing today.
Educating others and clearing the doubts of others as well as ours related to the field of environment and sustainable living. (That's what sustainability.SE does).
Discussing sustainability ideas, methods, tricks, policies of government to exploit natural resources and other legislations including talks at UNFCCC and other platforms, lifestyles etc. This discussions can help to conclude which steps to follow to protect environment, whether the policies and methods to exploit natural resources in the certain areas are right or wrong etc.
Encouraging others to take care of environment and live responsibly without damaging the environment.
Organizing public opinions, if needed, against any government policy or any industrial plants or undertakings which can have hazardous impact on the environment. (Arab spring is a lively example of the role social networking sites can play in mobilizing the public opinion). This can play strong role as a pressure group and will help to pressurize reluctant political leaders to take beneficial steps to protect environment.
The most important role for social media I see is to provide the alternative solutions to those that we are bombarded in mass media and advertisements.
The promoted model of life is
We can provide the tips, how to:
1) Save money by buying more consciously, and therefore less
2) Repair things, therefore use them longer
3) Reuse the things that are broken (for example use parts of old clothes for cleaning up floor or sealing up the roof)