Welcome to Reef 2 Reef!!
Never heard the term of Cured Coral, so gotta take a pass on that one.
If the rock has been "cured" and "cycled", then you should be able to add it.
Some forms of algae (chaeto) are beneficial to help phosphates or nitrates, but those are grown in a sump, refugium or a reactor.
Again,
Welcome to our reefing family!!