The crab should be moved because of the cycle, as well as for any kind of treatments. If you are treating the water with a hyposalinity for example, that crab is never going to make it.
As for the damsels, it is dangerous to them because you are exposing them to dangerous and toxic levels of ammonia that is burning their gills. When the fish eat and breate in the water, that waste turns into ammonia, and because there is not enough bacteria to convert that into nitrite, the ammonia will just keep going up ad up until the bacteria forms. It would be a little less if the live rock was cured, but most times LFS' do not sell cured live rock very often.
Me personally, I would just cycle with a dead cocktail shrimp and do it that way. Cycling the QT with a piece of live rock is a bad idea also because a lot of the biological bacteria is forming on the live rock. When you go to do a hypo treatment in there, you are going to have to take out the piece of live rock. Because you will be removing a large amount of biological bacteria, the ammonia will spike and new bacteria will need to be formed again, perhaps causing a mini-cycle to begin.
