Those that organize online, including signing petitions, are engaging in an effective form of protest. This attracts a lot of attention and spreads the word quickly. It may even get picked up by traditional media outlets. For instance, the recall effort against the judge in the Stanford University rape case has garnered a ton of attention from a grass roots online effort.
With the proliferation of the internet, online organization should be very effective. It might not be wise to only organize online considering not everyone has internet access, but since most people do it should be quite effective and efficient. Putting a message online is a good way to reach many people at once, and would definitely get your message noticed by many people.
Yes, organizing online is a very effective method of protesting something, and has been proven as such in the past with one notable example: the revolution in Egypt. During this Arab Spring revolution, protestors organized on Facebook and Twitter to plan their rallies and other protests that eventually led to the overthrow of the old government. Social media and other online platforms are in some cases the only form of effective organization for protest movements.
Organizing online is an effective method of protesting something to the extent that social media is the new medium of getting the word out. However, online protests are really a lazy man's method of protest. Nothing makes a point like being on a picket line. A bunch of anonymous complainers has far less effect.