You Can Implement Organizational Change without a Project Plan...

You can implement big deal organizational change without a project plan but experience tells us your implementation will be slower, it will meander off track, and it will include false starts all that will create what I call "change friction" or future resistance. No one wants more change friction than is already present naturally in a project.
As you are starting any implementation of a larger organizational change most sites or companies start with a gap assessment of some type then they look to close the gaps. It is a fairly simple process to get started. What happens next is where people diverge down different paths. Some build a comprehensive plan including all the task required to get from one level of performance to the next, others use the list of gaps as a check list and go after them one by one or in parallel. Some create a detailed plan but do not manage the implementation with it after the kick off and at least one organization believes you take off on your journey to increased performance and just discover your path along the way.
I will be honest and tell you that I don't enjoy Microsoft Project and Gantt charts and managing projects at the task level, but that does not mean that I don't (A.) see the value (B.) demand it with in the projects I am involved in, including the projects that are my personal responsibility. It comes down to dollars and cents, projects that have good project plans that are used consistently though out the implementation are less expensive to implement, provide results sooner, and have substantially less drama. I do hate drama.
So how do we build a good project plan to manage with? The Project Management Institute provides some great advice but here is a simple plan for creating plans:

First, take the gap assessment and list out the findings that you intend to address

Second, list any elements or task that will need to be in place before you can take the steps to close the gaps list. These are fundamental steps.

Third, add in the people and change management elements like a project risk identification exercise and then the risk and communication planning steps.

Fourth, look for natural order. What has to happen in what order to most effectively make the change occur. Link the task that must occur in a certain order.

Fifth, add in project management tools like metrics, resource requirements, and schedule them at appropriate points.

Last, be ready for change as this is a live document. You will add tasks as you discover them and you will change order of implementation due to unforeseen developments.

Now you are ready to manage the project. Stay on it! Track completion percentages. Share progress with the teams and the sponsors. Show project creep and time line extensions.

If you do even this simple level of project management you will see a faster project, with better results and less drama. If you still aren't sure you want to use a plan, then call me and I will share a few horror stories.