This is a sequel to my previous question How big could a moon be before its orbit became too unstable or tidally locked to its planet
OK, let's imagine that the thing everyone thought was a moon was actually a twin planet sharing a barycentre with BlinketyBlink.
They are currently not tidally locked, the twin is slightly smaller, with a similar basic composition and a Venus-like atmosphere.
They are far apart enough to not cause deadly disturbances on BlinketyBlink's geophysical conditions (weather, plate tectonics, volcanism, tidal waves...)
Everything is just perfect and life goes on normally on BlinketyBlink.
My question is : could the twins have an Earth-like orbit around their Sun? That's to say about 365 days, slightly elliptic and that would maintain regular weather patterns (summer to winter seasonal periods) on BlinketyBlink?