I'm not making a hard and fast prediction, but if Andrew is not invited to Sandringham for the Christmas celebration, it would be extremely petty on the part of Charles. He can discreetly arrive at Sandringham or he really could drive up and be seen arriving by the press...it's a private family celebration of the holiday. To leave him out would further hurt and embarrass Beatrice and Eugenie.
I don't see Andrew attending the Christmas luncheon which as I stated above, there's no reason for him not to attend, except for viewing the Royal Family members arrive and depart, the luncheon is a private celebration. I hope I'm proven wrong and we see Andrew at the luncheon and he goes to Sandringham. If he is at Sandringham, we won't see him walk with the family to Christmas morning service.