Yes, if you look at the RFC at https://www.ietf.org/rfc/rfc3261.txt
It explains exactly how to do this.
The Error-Info header field provides a pointer to additional
information about the error status response.
SIP UACs have user interface capabilities ranging from pop-up
windows and audio on PC softclients to audio-only on "black"
phones or endpoints connected via gateways. Rather than forcing a
server generating an error to choose between sending an error
status code with a detailed reason phrase and playing an audio
recording, the Error-Info header field allows both to be sent.
The UAC then has the choice of which error indicator to render to
A UAC MAY treat a SIP or SIPS URI in an Error-Info header field as if
it were a Contact in a redirect and generate a new INVITE, resulting
in a recorded announcement session being established. A non-SIP URI
MAY be rendered to the user.
SIP/2.0 404 The number you have dialed is not in service
The client would therefore receive the 404 in the SIP reply plus it will be told to connect to sip:firstname.lastname@example.org for a recorded message.