Nope.
AOL died because people had no personal investment in the service, beyond their AOL e-mail address. It became cheaper and better to get high-speed access via DSL or cable, and the custom content that AOL provided was of little value. So it was a no-brainer to walk away.
Not so easy with Facebook. If you walk away from Facebook, you potentially lose the ability to connect with hundreds of people, you lose photos and videos, you lose games and website logins.
The comparison is apples-to-oranges.