Yes, but ration them — sunflower seeds are safe yet so fatty and addictive that parrots will eat them to the exclusion of everything else.
What it means for conures
In moderation conures can enjoy sunflower seeds, but it's rich, so keep it to a treat rather than a daily food. A conure can handle a moderate portion.
The full picture on sunflower seeds
Sunflower seeds are the potato chips of the bird world: high fat, high reward, low effort. A seed-junkie parrot eating a sunflower-heavy mix is on the road to obesity, fatty liver disease, and malnutrition — the classic diet problem in budgies, cockatiels, and conures.
A few seeds a day, ideally hand-delivered as training rewards.
Unsalted, unroasted, ideally in-shell for the foraging work.
Especially strict rationing for budgies and conures prone to obesity.