NASA recently announced that orphan planets, planets no longer orbiting a star, may be more numerous than the stars in our galaxy.
The Sun's Hill sphere, its gravitational influence within the Milky Way, is ~2.2 ly. So it's possible, however unlikely, that a Jupiter size orphan planet could attain solar system orbit, say with a semi-major axis of one light year and a ~1.6E7 year period. The barycenter of this body and the Sun would, therefore, be ~60.3 AU from the Sun.
Could we detect the Sun's motion around the hypothetical Jupiter barycenter by its gradual anomalous displacement versus distant stars and therefore detect the existence of such a far-off massive planet?