Does my organization need adopt Agile Soft. Dev. before adopting DevOps?
Agile Software Development is not required to do DevOps, but I believe the argument can be made that the value proposition for DevOps is often a lot lower without Agile.

DevOps is a lot of things, but automation is a central theme.  The value of automation increases in direct proportion to the frequency with which Development creates new releases.  Frequent deployment has a positive impact on certain types of products, specifically consumer applications.  High velocity all the way through the software delivery lifecycle returns value for each iteration (anyone seen the CA ad where the zombies want new features in their apps?)

Without Agile, high-frequency releases are extremely difficult, if not impossible.  If the Development team is releasing software once a quarter, or twice a year, DevOps can still automate the process, but then what is the point?  The investment in time, training, and resources to adopt DevOps may be partly returned in quality, however, the best value is in maintaining high velocity throughout the delivery lifecycle.

One could also argue that if you're going to adopt DevOps, why wouldn't you also adopt Agile?  The principles that make them both work, work well together.  Practicing DevOps by itself, without Agile, could create an imbalance between Ops and Dev, in which Ops is outperforming Dev for service delivery.