ya the dome is a skeleton from a coral. the other thing in the pic may also be dead coral although its hard to tell.
you have to remember that there are LPS and SPS corals and that coral skeletons come in many shapes and configurations.
A sponge will look like... a sponge! kind of squishy looking usually or something- its hard to explain. but that dome is a hard calcium skeleton for sure. now, things may start to grow on it, just as if it was a piece of rock (kind of making it live rock at that point)= but its still DEAD coral.
There have been times where people have put WAAAAAY dead skeletons (like the dome one ) in thier tank and months later the coral came back to life. Usually thats only if the coral was 'recently thought to be deceased'. Im thinking you may have picked that out while it was dry seeing as its soooo white still.
In time it will be covered with coralline(hopefully) and stick some frags to it- it doesnt matter if its skeleton or rock- its a hard surface... but NOT a sponge!
Happy Reefing
Jess