It does not post to the timeline. It goes to a small section called Recent Activity. It is there, just not very in your face.
It's not there either. There's only three things in that section. Me liking a page about 17 hours ago, after the level up. Me doing something with spotify on friday, before the level up and something from the third.
I don't even understand why this is a thing. What possible benefit could there be for linking in-game activities and real world identity?
Absolutely none. Just like dyes, jawas and C2-N2. But like the dyes, some people enjoy posting their ingame stuff to facebook.