Gibson did do some custom-order guitars with CC pickups, but you're right- the instrument in my avatar (it was up on eBay some time ago, which is where I got the image) began life in 1957 as an acoustic L-5CN. The original owner had the CC pickup custom-installed in 1959. The late 50's was a time when the CC pickup had a resurgence in popularity, and a lot of the old stock of those pickups were made available by Gibson for such customizations. They also put out a very small run of L-4's (an acoustic archtop that looks like an ES-175 without pickups) with CC pickups, and those are extremely rare.
If you don't have it already, pick up Kenny Burrell's "Moten Swing" CD (reissue of the old "Bluesin' Around" album on Columbia). He used an L-5 with a CC on several tracks on that. A heavenly sounding guitar... especially in HIS hands.
I kinda suspected the L5 started off as an acoustic. Electric L5s, L7s and L4s from that time period had a really UGLY pickup arrangement, where the pickup was built into a really ugly pickguard. McCartey's ideas weren't always good.
Burrell has always sounded nice. Typically though he opts for a Super400 rather than an L5. Even back in the days of yore. I seem to recall most of the pictures of him featured a sharp cutaway Super400.