Could two objects be caught into an orbit around some kind of dense object, perhaps a rogue planet. Could they share an atmosphere.
So how much do you know about drag? Orbits in atmosphere are short lived - as reference see any low earth orbit satellite. They need regular boosts or else they fall in.
So your objects could orbit... Briefly.
But not in the way you have drawn in the diagram, and not for any length of time.
Basically it's a no, in any real terms.