Yes, with care — human-grade, shelled, unsalted peanuts are okay as an occasional treat. The risk is aflatoxin, a mold poison that causes liver disease in birds.
What it means for African greys
In moderation African greys can enjoy peanuts, but it's rich, so keep it to a treat rather than a daily food. Greys can take a larger portion than small parrots.
The full picture on peanuts
Peanuts themselves are not toxic; the danger is Aspergillus mold, which produces aflatoxin and thrives inside peanut shells — especially in bulk bins and bird-feed-grade nuts. Chronic low-dose exposure causes liver disease; a moldy nut can cause acute poisoning. Peanuts are also fatty enough to crowd out better foods.
Human-grade, shelled, unsalted, unflavored only.
Use as occasional training treats, not a daily staple — a half peanut for small birds.
Discard anything discolored, shriveled, or musty-smelling.