This is really neat. Mark Atherton has put together a very basic, working, replica of a base station for analog cellular phones. I've blogged about something similar for GSM phones in the past. This analog system is pretty fascinating for me.
We really have the parts to put together something basically similar for ham radio. The audio could be exactly the same as it is now. Add in a control channel and people could call you even if you have the volume turned all the way down. There have been in-channel methods for quite a long time of course. Signalling systems such as CTCSS, DCS, DTMF have been constructed in the past, and barely used. As of yet, noone has constructed an out-of-channel signalling method. The capability is there for APRS I believe. Some APRS capable radios can advertise a frequency you are monitoring in your report. I think one or two may even allow you to QSY to an advertised frequency.
It'd be pretty cool if you could send out an APRS call, have the other parties' radio QSY to your freq if they answer it, test the path, maybe QSY to a mutually accessible repeater if necessary, etc. I have no delusions that this would be constructed or used though. Previous in-channel signalling methods have been around for decades and remain fairly unused, except to access a repeater. Other neat technologies have falling by the wayside, like Kenwood's DCS-based ID tech.
You know what they say, a rolling stone gathers no moss.