Question!

winners are already chosen at random here, why would you need random.org to pick one? you can't pick winners at all, unless you reroll over and over until you get whoever you want to win... but you need a valid reason to reroll in the first place.

you could make a private giveaway and give the link to people, but i don't know if you can do that to promote your facebook comment...

The latter, perhaps, if support approves it (you'd have to submit a support ticket). The former, not if you want credit/CV for it, it'd have to just be some sort of forum giveaway

Answer!

No.
You could open a topic to make a giveaway using random.org (it won't give you any CV) but you might need mod approval for the facebook requirement.