I think most of us remove all of the outer shell (Neal and I have found that buying them with the shells on seems to make the meat more acceptable even though it is offerred with shell off) to avoid having to hunt waste after dinner. I have wondered, however, if small amounts of the shell would be beneficial.
I don't know and I keep hoping one of the grad students will do some kind of nutrition study .
Since octopuses don't have bones calcium doesn't seem to be important and the beak is something akin to fingernails so I keep wondering what might be beneficial that they naturally acquire in the wild (looking up food additives to help human nails did not help me much). At this point the experienced recommendations are "no additives" since we can't distinguish between helpful and harmful. Exoskeleton inclusion may or may not be digested, should fall on the harmless side but may have absolutely no benefit. It is, however, important to remove uneaten remains and shrimp remains are on the high end of ammonia creators (I don't think the exoskeleton and head are the major culprits though). When I fed Octane live shrimp (full sized, not shore shrimp), I did not find anything to remove but my clean-up crew may have handled the left overs.