Slimserver doesn't do that natively. You would have to write a program to automate the process (autoplay -> CD extraction -> encoding -> database import -> playing new tracks). And even if you did automate it, that CD would now be a part of your collection, which violates one of your requirements. You have to bite the bullet and rip your CD collection ahead of time.
When I ripped my CD collection, I went through the thought process of, "should I even rip those CDs I hardly listen to?". Most of us have CDs we keep around for sentimental reasons and don't listen to much. The conclusion I came to was, "rip them all". Disk space is so cheap these days that the incremental benefit comes at almost no cost.
I retired my CD player to its original box in my closet, BTW.