Yes — grapes are safe for parrots (unlike for dogs), but they're mostly sugar and water, so treat them as an occasional sweet, not a staple.
What it means for conures
Take extra care with grapes for conures — read the full reasons below before sharing. A conure can handle a moderate portion.
The full picture on grapes
The grape toxicity that worries dog owners has not been observed in parrots — grapes are safe for birds. The real issue is sugar: grapes are candy-sweet, and birds will fill up on them at the expense of vegetables and pellets. Raisins concentrate that sugar further.
Limit to one or two grapes, a few times a week.
Halve them for small species, and wash well — grapes are heavily sprayed.
Seeded varieties are fine; grape seeds are not toxic to parrots.