well, they may live, but i wouldn't have coral in a tank that was cycling. that guy lied to you.
now that they are there, you might as well leave them.
btw, an important word of advice:
don't add corals to the tank unless you really, really, really, like the look of them. i've seen it many times- folks adding live coral just to have living things in the tank and they turn out to be ugly brown, or quite invasive, or both.
like kenya tree for instance. kenya tree coral is not attractive at all. people add it because it grows fast and is super hard to kill.
it's a mistake to add it to your tank, if your plan is to have a beautiful reef.
you will be surprised how fast you run out of real estate in that tank.