A good surveyor who knows what to look for would likely find any problems; but some might not (might not look; might not look thoroughly enough; might not know what to look for). What I am saying is not to just blindly assume all surveyors are equal and all would find a problem. (I realize you are not blindly assuming or you would not be asking!)
My background in this is in buying a small boat long-distance, many years ago. I looked up a qualified surveyor online (NAMS or SAMS certified, I forget which), contacted him, and explained what I was looking for in a survey. The two things I was most concerned about were hull blisters and core damage. The survey came through with flying colors, and I bought the boat. Drove cross country to pick it up only to find... yep... hull blisters and obvious evidence of deck core issues. Being a bit younger and more innocent (and having recruited a friend to drive down with me), I went ahead and bought it. The one good thing I can say is that I learned a lot about working on fiberglass boats; but I was actually looking to go boating! Nowadays I would have requested more detailed photos and etc., but this was early days online (and in my long-distance fiberglass boat buying experience)
Now I often find that on a relatively simple boat I am my best surveyor (and if I were less confident in my abilities I would still do my own survey in addition to hiring a pro). There are things you can check yourself if you are so inclined, and no-one cares as much as you.
As far as I know, none of the C-Dorys were built with specific core protection (which is the same with most production boats, so not picking on them). So what you find will be dependent on owner maintenance or improvements, storage method (or climate), and some luck. My guess is that most of the boats don't have catastrophic core damage, but many have some (that can be relatively easily remedied). By that I mean a bit of damp core around certain hatches and that sort of thing.
The main cored areas are the transom, the hull bottom (forward to around the helm bulkhead), and the decks. There is some additional core in the "walls" and some boats have core in the cabin top (in varying places). Obviously it's where there are penetrations that are of most concern, especially beneath the waterline or on the sole (where water can collect).
A good set of eyes looking for telltale signs is great; a good moisture meter can help; and the ultimate is actually looking at the core (removing fastener or fitting).
Anything that gets bedded/caulked is something that needs periodic renewal (hatches, deck fittings, through-hulls, etc.). As built, if/when the bedding/caulking fails then the core in a cored area can take on water. Many of us go on to seal or close out the core (in a variety of ways). After that, water that gets past bedding is a leak that needs to be taken care of, but should not get into the core.
I hope this wasn't more info than you were looking for! Also, in case I wasn't clear about it above, there are some excellent surveyors. Just don't assume all are equal.
Sunbeam