It is my opinion that is possible to celebrate Christmas and Hanukkah without paying tribute to God. I feel that some people can lose sight of the reason for these holidays when the time comes, and focus only what takes place during the holiday. They focus on the food, gifts, and people they will see instead of the reason for celebrating the holiday itself.
Christmas? Sure, I think anyone who wants to put up a tree and sing Jingle Bell Rock while getting trashed on eggnog and swapping presents should do so. Hanukkah, well, not so much. Unlike Christmas, which was a fabricated Christian holiday, Hanukkah has religious meaning. I can't see you separating it from the tradition.
I believe many people celebrate Christmas and Hanukkah without actually paying tribute to God. I know my family celebrates Christmas every year, but its merely a secularized version of the Christian holiday. I believe these holidays have been commercialized to the point that their religious roots are no longer part of the ceremony.
I think it's very possible to celebrate these holidays without including the religious element, I think that the act of giving gifts and spending time with your family on these holidays does not require someone to pay tribute to god, It's up to everyone on how exactly they wish to celebrate these holidays.
No, it is not possible to celebrate Christian and Hanukkah without paying tribute to God, because a person who chooses not to acknowledge God but tries to honor the holidays is honoring something other than what the religion actually stands for. Those holidays are holidays for celebrating God. Those who do not are not truly honoring the celebration of God.