I mean, all birds are (avian) dinosaurs and descendants of (avian) dinosaurs that survived the drastic climate change that caused the extinction of (all non-avian and many avian) dinosaurs caused by the asteroid impact.

The question is, what are dragons? If we go with the likes of Komodo Dragons and all dragons being relatively closely related to them, then unfortunately, birds are not dragons and not even closely related.
But if we go by the explanation that the dragon myth is a consequence of dinosaur bones and skeletons found by early humans, then yes, magpies could fit right in with dragons.