It may be possible with some radio systems, but it's not likely with others. At LAPD for example, the unit's callsign (like "1-Adam-12") is not electronically transmitted, but rather the
radio's unique identifier.
Before the officers begin each watch, the CAD system is given the call sign, vehicle "shop" number, each officer's serial number, and the 4-digit serial number (LAPD calls them ROVER numbers) of each of the two or three radios assigned to the unit. With a few exceptions, all the ROVER/radio numbers for each unit change every shift.
When a transmission is made, only the ROVER number accompanies it, and it's not until it reaches the CAD system at the comm center that the unit's ID ("1A12") is attached and displayed for the dispatcher.
Except for occasionally when they may have to log on verbally for some reason, the listener has no way of associating any specific radio's ID with its unit ID number, and
that would be possible only if the scanner can decode the ROVER number. That part probably wouldn't be a big deal, though.
I don't think I'm expressing myself clearly. If I can still get in and edit this tomorrow I'll try to do it.