The ability to interpret groups in the .obj file depends on the receiving software. We cannot answer about the compatibility of other software, but at least for Blender, groups of obj files output by Blender itself cannot be read, so it must mean that Blender itself does not support the group in the importer.

The obj's .mtl file stores the "diffuse color", which differs from the combination of the "base color" and "diffuse value" in Metasequoia. Therefore, irreversible conversions occur when loading the .obj/.mtl file, and it is not reproduced as per the original values. The same is true for other software and file formats with different color and value representation formats.