Yes, unconventional participation is a natural right for citizens in a democracy. Of course, this is just an opinion as there is no way to know if natural rights exist or, if they do exist, what they are.
Most people would argue that the freedom of speech and expression is a natural right for all people. It is a right that must be respected if a country is to be called a true democracy. Unconventional participation is clearly one type of expression. As such, it should be protected as a natural right.
Unconventional participation is an important type of expression. It is particularly useful for people who do not have a great deal of conventional power. If we were to take away the right to unconventional participation, we would be robbing people of an important way to get their ideas across to government. We would, for example, be taking away the method of expression that allowed the Civil Rights Movement to gain rights for African Americans.
Clearly, unconventional participation is an important form of expression and is, therefore, a natural right.