I don't think the basic premise flies. The dryad is able to walk around without carrying the tree because she is (part of) the spirit in a separate physical form. Teleport only affects the physical form; you can teleport someone's body whose soul is Soul Trapped or Magic Jarred and the soul doesn't go anywhere. Or you can move the soul container, and the body doesn't get moved. (Either might have bad effects, just as it might for the dryad, but it doesn't physically drag the other half along.)