Hello,
I understand that you're wondering if an OBJ file can contain vertex weight information for a bone animation rig (for import or export.)
To the best of my knowledge, I don't believe it can. The OBJ file format is fairly old, and I don't see any vertex weighting or bone assignment data present in either the Import or Export settings of 3ds Max. You can embed material assignments, colors and UV mapping coordinates, and other types of simple data with the OBJ export, but not bone/vertex weights and envelope information.
I think your best bet would be to try to use Collada .DAE or .FBX file formats for animation model file exchange. The Alembic .ABC format may also work. However, these formats may just allow you to bake/export existing animation data into your meshes, and not vertex/bone weights and envelopes themselves.
Please let me know if this information helps.
Best regards,
Jon A. Bell
Autodesk Technical Support
Jon A. Bell
Senior Technical Support Specialist, 3ds Max