I think divestment definitely has its place, but its effectiveness will depend on what is being protested. There are certain times when the thing being protested will welcome divestment and therefore it will be useless. Other times divestment can be the most effective way to make a change and be noticed.
Divestment is a sucessful form of protest against countries and people that rely heavily on finincial assistance. It is similar to sanctions, and it has been successful in places like Iran, and South Africa during apartheid. It has also been used sucessfully to protest environmental issues. Despite this it is not effective if finances are not a concern.
I guess it all depends how much money a person has with a company. If you do not have that much money invested in a company, then they probably won't care as much. It would grab their attention at the very least though. Hopefully, it would make them change their ways enough because they would not want their more high end clients to do the same thing.
Even if companies threaten to divest in a local area, the maneuver serves as a form of protest. Divestment removes economic activity from an area, which in turn reduces jobs and leaves more people without viable incomes. Divestment is also a means of protest because entire groups of people can boycott certain companies and affect their bottom lines.
I think since it in sense is an opposite of an investment, it can be used as a form of protest. I think it would be kind of childish in nature,but it still serves its purpose. I don't see how it would be an effecitve means of protest, nobody would take you seriously.