While they still have not had the official press Grand Opening, Monsters, Inc. is being advertised to guests as "NOW OPEN!".
The Disneyland Guide to the Magic that was released today has that comment in LARGE Yellow letters.
You see this large banner when you enter the west side Security gates.
They have removed the "preview" comment on the ad they had in the middle of the Main Entry Plaza.
Plus on the side of the ticket booths is this.
So except for the morning hours on Monday January 23rd, you should be able to ride Monsters, Inc. (Of course, like any attraction, it could be closed due to mechanical issues)