Doc Planning is as important as the Dev/Feature Planning.
The Doc Plan should be part of the overall release plan.
Without documentation, the client may not know how to use your product. The client may not even know that a feature exists.
A product is not ready to release if a doc is not ready.
The reason is simple. The doc is part of the product.
Because of the doc is part of the product, it should also have the quality assurance process. When a QA tests the product, the testing should include the testing of the documentation.
It is a commonly seen problem that the development pass the instruction about how the product works to QA and QA does not look at the documentation at all. The reason is that they do not need to since they already know. However, those information that the Dev team pass to the QA team are not documented anywhere and thus not covered in the documentation.
A disciplined QA will know and ensure the accuracy of the documentation.
The release manager should have the doc ready as a release criteria. The doc ready is not based on whether doc team finished writing based on their knowledge. The doc ready should be based whether the doc is reviewed and TESTED.