Directly to Voicemail

Is it possible to leave a voicemail without letting the phone ring?
i.e. A calls B and leaves B a voicemail without ever having the phone ring.

This is typically something that is done on the server via dialplan / configuration. Just set things up in such a way that a caller goes directly to voicemail without initiating a call to the phone itself.

Typically this is what the DND status is for. The user sets that in order to have all inbound calls directly dumped to voicemail.