I have received such a letter below on Jan 18. And my status on the website is "complete"; all the materials are received.
Dear XXX,
Your application for admission to the UCLA Anderson School has been processed. Included in this email is the 12-digit status ID required for checking the status of your application:
Be sure to save this email so that you can subsequently access your 12-digit status ID.
We appreciate your interest in the UCLA Anderson School and assure you that your application will be given careful consideration. If you have any questions, please refer to our website.
BTW, I know some R1 applicants received the admmission already, while the R2 process seems to be very slow and everybody is waiting. haven't heard that anyone got an invitation now.