They will, being that the multiplayer in Anniversary is just basically a cut-out playlist from Reach. Hitting "Multiplayer" on the Anniversary main menu will just jump you into a version of Reach's multiplayer in which only the remake maps and Anniversary
playlist will be available. :)
[quote user="I MX Rider I"] Will your rank and stats carry over from reach? [/quote]
Yes, because the multiplayer is Halo: Reach. It's a separate disc with the entire Halo: Reach multiplayer on it. Think of it like Halo 3: ODST and how it came with a Halo 3 multiplayer disc - the complete Halo 3 multiplayer.
This is going to be the exact same situation. So yes, everything will be the same because it's the same game.