Doesn't seem so. While they set her up in a similar position to the show thanks to Rebirth paving the way for that availability, it isn't the show's world. Which they confirmed. Both with the League of Shadows and it's existence in this world when in the Arrowverse, they don't, along with the fact that in Supergirl, aliens aren't really allowed to freely roam in public while Brainy does here. Plus Dreamer's energy blades here while in the show, she launches dream energy out of her wrists.