NO, because you notice, they still say "Happy New Year." Happy Holidays is a phrase that's being used in order to consign "Christmas" down the memory hole. It's being used by people and businesses who either share the values or, or are intimidate by, PC and anti-Christmas elements, groups who are at war with our cultural traditions.
When the term "happy holiday" is used, it is being used to wish nothing more than "happiness." Nothing more. There is no implicit condemnation of Christmas, and nothing is being consigned down a "memory hole" .. whatever that is.
Take happiness and joy where you can get it. Peace, too.