People did (over 80k pieces of mail on one day alone), and they were greatly appreciated.
Noah is now in his last days, and his family has requested that people stop sending cards. Snopes.com reports that family requested no more cards or gifts:
Please publicize this in your communities (real and virtual). A quick tweet or a facebook update would do a lot to keep a postal tidal wave from complicating this family's final days together.
Wow! The outpouring of love and concern for Noah is justPLEASE STOP SENDING CARDS AND GIFTS!!!!
amazing! Scott and I never in a million years thought that so many
people would want to send Christmas cards to Noah. However, please
note: We did already celebrate Christmas LAST Sunday -- November
Noah is very ill. He is not getting out of bed and it's time for
Scott, our families, and I to concentrate on our son. His time is
very short and he needs us.
Let's have second Internet miracle and put this Christmas card genie back in the bottle.
If you want to do more for Noah and other families facing the same horror, donate a dollar or more in his name to the Children's Hospital of Michigan Foundation.
The full snopes.com post: http://www.snopes.com/inboxer/medical/biorkman.asp
Noah Biorkman's Care Pages site: https://www.carepages.com/carepages/NoahScottBiorkman