While I haven't tried planting sunflowers in the winter... My experiences with them suggest that they know when to come up...
Down where I am in GA... I can take the seeds of most veggies... and plant them as soon as they mature... and they come up.
This means multiple generations in the same year!
Not so with sunflowers...
Any sunflower seeds from the current year... wait until next year to come up... even though there is plenty of time!
I suspect that winter sown sunflower seed would lie dormant... until the correct time for growth, and probably get over-planted...