Is it possible to coarsen a uniformly refined mesh, as well as an adaptively generated mesh?

Yes. However, the user needs to add some seed nodes.

The coarsening algorithm can operate on several regions of the mesh. Each region must be identified using a “seed” node. The boundary of each region is automatically computed to include all elements that are connected to the seed node, and all neighbors that have an equal level of mesh refinement. In this way, a narrow band of mesh refinement extending across a part will divide the part into two regions, and a seed node must be identified in each region that is to be coarsened.

If the mesh is obtained without adaptivity, then it could be regarded as one region, and we just input one seed node.