With IceCast all you really need to do is connect via your live source dj. This will then mount point from /stream to /live and the live dj will be heard right away. The AutoDJ continues to play in the background. When the live source disconnects the AutoDJ which is still running will just play through moving forward until the next time someone else connects live.
Does this work for Shoutcast as well?
It really depends on which ShoutCast version you are using.
SHOUTcast DNAS v2 with sc_trans v2
Yes, this is natively supported by DNAS2/sctrans2. Your live DJs actually connect directly to sc_trans v2 (instead of to the SHOUTcast DNAS v2 server) and when sc_trans v2 detects a live source connection, it stops performing its autoDJ duties and just passes the live source through to the SHOUTcast DNAS v2 server.
This is all seamless for the DJ and listeners if you use the instructions on the Quick Links page for connecting with a live source.
Shoutcast DNAS v2 with sc_trans v2 does support the live transition natively. The way this one works behind the scenes is when your live DJ connects they are just connecting straight to the sc_trans v2 instead of the ShoutCast DNAS v2 server. When the sc_trans v2 detects a live source it just stops broadcasting the autoDJ and sends the live source through the ShoutCast DNAS v2 server.