The artist ships Vegeta and Goku, and if I recall correctly they did have beards in one episode of Super. So I'm tagging them this way for now.
Yes, after they got out of the Hyperbaric Time Chamber.
Also, I don't think Bardock was ever shown with a beard (with that huge scar on his cheek, it is quite possible that he is no longer able to grow a beard that would look even or attractive).