Could a star revolve around a planet?

And the whole barycenter thing too.

You're throwing out the definition of orbit at this point, and moving into a different realm. If you throw out barycenter, you have to leave me with my frames of reference.

A star can definitely orbit a planet, if one such as this did in fact exist. You are assuming it is simply a planet-star system, which makes things easier. If you're on the planet, the star is orbiting you, if you're on the star (ouch), the planet is orbiting you.

Once they are of comparable size, the barycenter thing has to be taken into account, you can't just throw out this crucial part of the physics, even in a thought experiment. If you want that part out, the planet must be much bigger than the star.