Hmmm.... Do you have growing lights or a light set up of some kind? I just don't think you are going to have a south window that is going to even come close to the amount of sunshine it takes a sunflower to grow and be happy. You can try, but I wouldn't look for much. If you can at least limp it along during the winter, maybe once you plant it outside it will do better and you will not have lost the strain.
