Maybe it's me, Android 4.4, BBS misreporting, or the latest FB betas, but Facebook doesn't wake the phone at all anymore if you turn off notifications. I depend on email notifications anyway.
This was a huge issue a few months back though and even with Greenify, I could see it peeking out with wakelocks.
It just stays greenified for me. I don't care for facebook notifications in the least, but the app is easier to navigate on my phone than the website. And the app wants to use the GPS way too much, even if you don't ever check in.
Their app has not ever been on my tablet, and I intend to keep it that way.
They are far too large a tech company to be taking this long for their Android app to approach decent, let alone good. Like the verge and so many others, they just don't care.
4.4 is supposed to help reduce wakelocks though by forcing apps that wake the phone to do it en masse instead of whenever they please. I'm sure that's helping quite a bit.