Yes, but ration them — sunflower seeds are safe yet so fatty and addictive that parrots will eat them to the exclusion of everything else.
Keeper's noteFlip the script: pull them out of the food bowl entirely and use them one at a time as training currency. A sunflower seed earned is worth ten free-fed.
What to watch out for with 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.
How to serve it
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.