The Streisand Effect is the term used to describe the way in which attempts to supress or censor content can sometimes have the paradoxical effect of promoting its spread.
People have a natural interest in things which other people want to keep secret. Also, the censor is usually percieved as a big bad organisation; the censorship is seen as a violation of free speech rights - and the Goliath effect kicks in.
Is it possible that the Streisand effect could be used for marketing purposes?
One possibilty is the censoring organisation may conduct the censorship - in order to produce publicity for themselves. Usually, censorship shows them in a bad light - but if they believe that there's no such things as bad publicity, things might still go well for them. Ralph Lauren seems like one example of this:
They issued DCMA takedown notices to prevent their impossibly-slender model from being spread around on the internet. The result was an explosion of their content on the web. Ralph Lauren apparently liked the effect so much that they repeated the trick with another model. These days if you search for Ralph Lauren model copies of those images head the list.
The other possibilty is that the censored organisation may release controversial content deliberately - in the hope of generating publicity. Controversial content gets circulated for many reasons besides the Streisand effect - but if the content is censored, that is sometimes the icing on the cake.
An example of this:
But of course Moore was playing a very clever game: “I thought I lived in America, how could this happen!” he was saying, while laughing all the way to the bank. This is the best PR his film could have ever gotten – being censored was the best thing that ever happened to Fahrenheit 911.