There have been people who have had birds and Savannahs, there have also people who have lost their birds to Savannahs. It all depends on how you set the scene. You need to understand that Savannahs descend from Servals, and birds are one of the major food groups for Servals so natural prey for Savannahs. If your parrots are kept in cages and/or in a room where the Savannah cannot reach them then they will probably be safe. If you expect them to live together in harmony side by side... well I wouldn't hold my breath on that...
I don't know what kind, or how big your parrots are, but either side could probably cause damage to the other. Even if the parrots 'taught' the the Savannah to respect them at a young age and they did fine for months or even years, it only takes a particular flutter of the wings, or a darting movement of a bird to trigger the hunt instinct in a Savannah...