Have heard of a custom solution Avaya CSI did for some customers using IVRs. The calls would queue to agents, the IVR program would monitor the agent station and conference on an IVR port, play an announcement based on who the agent is and which VDN queued the call, then dropped the IVR and the agent continued.
It is a wise investment as it ensures consistent greetings, and reduced agent fatigue (gives agents a few seconds to catch their breath between calls). It also ensures agents are aware of which VDN was called as they hear the same greeting the caller hears and can start right into their script or routine.