Craig, I'm happy to let you know that this feature will be available in the very near future! Please keep an eye out for the next app update. We'll have live leader boards, real time golf league/group scoring and more. A virtually unlimited number of players will be able to track and view scores in real-time. People off course will be able to follow the round as well.
I believe the answer is yes, but see previous discussions on this in the Feature Request section:
"Leaderboard and betting"
See Keaton's response (the forum moderator) in the above. I would think round sharing through FB or Twitter is different than a live leaderboard functionality.