After a discussion with some members of the swatkats.us forums, I've decided that the petition probably isn't worth doing.
One reason is because there isn't much publicity about the petition. Therefore, Warner Brothers is unlikely to know about it.
The second reason (this was thought of by another forum member) is that it's too easy to have one person sign the petition more than once (using fake information). Thus the authenticity of the signatures might be questioned by WB.
So I've decided to abandon the use of the petition.