Everything orbits a barycentre. The position of that barycentre within or without the primary is not really relevant within several orders of approximation—and when it does become relevant, then that system becomes interesting in itself. Chances are the planet in question is so massive relative to its primary that we need to ask a more fundamental question: are we even looking at a star-planet relationship, or is it closer to a binary star system? Then we can investigate how that system formed and developed, and generalise and improve our model of stellar/planetary system development.
[delayed]