Is it normal for the concrete covering my interior perimeter drain to be damp?
Ideally, the builder installed a vapor barrier under the whole slab including the drain but it sounds like they cut a hole in the barrier to dig the pit for the sump. Since concrete is fairly porous, it's probably wicking water from the ground. If it bothers you, try a sealer intended for concrete with your problem. Unfortunately, you can't tell how much pressure the water is under because it evaporates or runs into the sump. Although it shouldn't be much, it will still wreak havoc with surface coatings.