Not quite.. I ordered a second Echo Dot for my mom last Thursday (the 15th). It was originally scheduled to ship on the 30th, but shipped early on the 19th and she got it today.
She's not very technically oriented (iPad is about as complicated as she wants to get), but absolutely LOVES the Dot. I bought her first one for her birthday back in October, and she called me on my birthday three weeks after that and had it sing "Happy Birthday" to me over the phone. She'd had it for all of a week before she told me "I need another one of these for the other end of the house.."