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 budgies
Because budgies are prone to obesity and fatty tumours, treat sunflower seeds as an occasional, rationed treat rather than a regular food — a little goes a long way for a bird this size. A budgie portion is tiny — a single bite or a little grated amount is plenty.
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.