Not in my case. I bought one bag from them in early November and surely was in their maillist after that, bot no promotions for Black Friday or X-Mas after that. They may do their own sale later though. I'll keep you posted if I receive something.
Burberry won't be having sales on their online website anymore, nor have they given promotion codes. However they may send you an email about discounts in-store after Christmas (apparently some python accessories are already on sale).
I would recommend buying from a different website that sells Burberry items such as Saks, Barney's, Louisa Via Roma. They often have reduced prices on Burberry products.