I'm not sure if there's any way to check how long a user has had an account on Facebook. I'm also not sure, if that information is available, if you'd be able to use that to deny a user access to login functionality. Facebook's terms don't really like you to restrict access to some users based on certain types of information, and I believe this would qualify.
Either way, in general, Facebook doesn't have a lot of 'fake' accounts. While there are some, Facebook vets the accounts pretty well and does email verification before they can ever register on your site. Accounts that get flagged for spam are also taken care of quickly.
Are you having a problem with 'fake' accounts from Facebook, or are you just trying to be cautious? Fake accounts from Facebook has not really been a concern for us in the past or an issue that users have raised with us.
Thanks,
Alex