I'm an engineer on the Facebook Messenger team.
Quick answer: Messenger does not sync your contacts to the server.
Official answer to the inaccurate meme that's going around: https://www.facebook.com/facebook/posts/10150353502026729
You might wonder how we match up your Facebook friends with your contacts so you don't see duplicates in the list: with Messenger, instead of doing it on the server, matching and de-duplicating of Facebook friends and local address book contacts is all done on the client.
The only time Messenger will send a phone number from your local address book to the server is when you use Messenger to send an SMS message to:
1) A non-Facebook user, or
2) A Facebook user who doesn't have a mobile contact point already on the server