Since people increasingly live their lives online can I be yotzei the mitzvah of bikur cholim by visting the choleh's Facebook page?
Yes, this fulfills the mitzva. As the g'mara says:
כל המבקר חולה נוטל אחד, מששים בצערו
Whoever visits a sick person washes one hand; they are feeling his pain.
Obviously this is not referring to visiting in person. As signs all over the hospital inform you, you should wash both hands when visiting in person. So it must be referring to visiting on Facebook.