Is it possible for an organization to operate in  a state of disorder due to absence or nonrecognition of authority (e.g., social, family, corporate, charitable, etc).  

The answer is a resounding yes and many of us can probably think of examples.  At first impression such an operation might be considered inefficient. 

Accepted Practices

Organizations define processes for conformity, quality and efficiency.  To some degree this boxing of how things are done can stifle innovation and creavity. 

If consistency is not a top priority and timelines for outcomes are nice to have but not critical cultural anarchy can define the processes, and is intended to do so. 

That is, anarchy is a choice rather than an accident.  Like most extreme practices, approaching absolute disorder (total anarchy) is probably not a good idea, but balancing loosely defined processes within the context of some level of constraint can lead to positive, even powerful, results. 

Collaboration and Anarchy

Working in a group with defined authorities and simple operating principles that are easily understood by all (ground rules) can be the underpinning of collaboration. 

Drawing the best of everyone on a egalitarian basis is a goal of collaboration.  Reducing the structure and allowing for some level of disorder might make achievement of desired outcome more challenging but on the contrary side they may well be better outcomes. 

Caution

This is a cautionary tale to some extent.   It is true anarchic approaches bring some merit to an organization processes and practices, however, on the flip side lack of structure can lead to some chaos. 

Blind anarchy might not bring the desired improvement in outcomes.