The only thing about shocking it with the cover on is that the fumes may damage the cover. If it is easy, maybe they can lift up a corner of the cover for awhile after shocking to let it vent and then recover it a day or two later? (Make sure you aren't expecting stormy weather at the time the corner is peeled back so the wind won't get under it and pull it off.)

One other thing, you might want to add some Polyquat 60% algaecide. It doesn't do too much for you if you already have algae, but it is a pretty good preventative.