A couple of years back I decided our 1976 LRC needed a "Divers Dream Plate" installed underwater on the transom centerline. I proceeded to drill two 1/2" holes in the appropriate spot on the lower transom. There was white foam coring where I drilled the holes. All nice and dry as the day installed. I cleaned out the foam about 1" all around, packed it solid with West epoxy, redrilled the 1/2" holes and completed the job. Since the transom is exposed on the inside you are able to see there is more foam coring. The areas where the swim platform bracket bolts come through the transom, the main engines exhaust, and the generator exhaust are isolated with no coring.
Second, probably 20 years ago a friend had a 50 Hatteras MY and was slowly taking on water. I helped him locate the leak under the starboard bunk in the master stateroom, where a through hull fitting had been mounted. There was definitely thick foam coring at this spot, installed as the hull was laid up. He had the area dug out, filled with more solid glass, and all was well. But Hatteras has definitely used foam coring on the hull bottom in this one case.
In 15 years on our LRC I have only found foam on the transom as described. None on the bottom or hull sides.
Pete