On pre 6.0 systems you cannot make CID display on the phone automatically before picking up the handeset.
6.0 and above gives you the programming option "Caller ID Y/N" on a per set basis. Pre 6.0, if the line is programmed as a ringing line on a set, the user can press F811 and see the caller id before answering, or you can program F811 on a button for a single press.
Pre 6.0 only gives you the option to define one telephone as the CID set, and that is defined under the "Lines" heading on a per-line basis.
What concerns me is your description. You mention a seperate "wiring box". That sounds to me like a 616 or 824 with DR5 software and a CID unit, not a compact ICS. If that the case, I've slept too much since then to comment.