Yes — ripe gooseberries are safe and rich in vitamin C and fiber. Their tartness divides birds, but it's harmless.
Keeper's noteA nice low-sugar berry for variety. Some birds find the sourness off-putting — try a few and see.
Why gooseberries is good for parrots
Ripe gooseberries are non-toxic and bring vitamin C, antioxidants, and fiber. They're quite tart, especially green ones, so some birds love them and others pass. Offer them ripe and washed; halve for small species.