Namo Buddhaya!
Pinwath mithurani,
It's OK to use any morally correct means (including the Facebook) to spread Dhamma
I personally believe that more effort should be made by the lay disciples to spread Dhamma over the Internet; as not many swaminwahansela should (or can afford to) spend time in the Internet.
e.g.
Facebook page: Mahamevnawa Buddhist Monastery (a page I like to promote

)
Another thing, as one friend has correctly pointed out, there are many accounts on FB impersonating famous people.
So we should be careful when accepting what promoted in the Internet.
Always check against Dhamma & Vinaya; to be on the safeside,
If anything helps cultivate Kusal & eliminate Akusal it's probably Dhamma
If anything helps us realize the Anithya, Dukkha & Anattha nature of the world it's likely to be Dhamma.
Still, we should develop a body of knowledge on Dhamma (Sutha) to exactly verify what we see on the Internet is Dhamma or not.
Theruwan saranai!
Namo Buddhaya...
related thread:
http://www.elakiri.com/forum/showthread.php?t=85283