Of course, if you don't answer your cell phone it goes to voice mail and plays your pre-recorded message.
But what we need are phones which can answer and play a pre-recorded message for a short time. In particular a message of the form, "Hold on, I'm in a meeting and must keep silent. However, I'm walking out of the meeting right now while you hear this recording, and in a few seconds I'll be able to talk to you. Hold on... Still walking..."