Yes....we've had that experience too. Once one of our males got spooked and flew several houses over. A family member went searching a while later and found him in a cat's mouth. The cat dropped him and ran, and they got him back. He healed up quickly and is still with us.
Quail are generally quite flighty and not friendly like chickens are. There are exceptions though, like @MageofMist 's male coturnix Scrappy.
I present you, my daft dumpling of a quail. He started off more aggressive than he was flighty, as he used to run up at me chattering and try and attack my feet. But he mellowed out over time and became a potato bird.