Yes you can, and should cycle amd cure the rock at the same time.
I would save the coralline for later though. Add this once the cycle is complete.
I would add a piece of raw shrimp into the tank once you're all filled up and the rock scape is set. Remove it after 24 hours or so. While you're waiting for the cycle to finish, get used to using test kits. Test your ammonia at first. As it starts to drop, test nitrites. Once that starts to drop, test nitrates. Once you hit 0 on ammonia and nitrites, you should be good to add a fish. Doing a 20% water change before adding the fish wouldn't be a bad thing. Make sure you start slow. A fish every month is good. Perhaps 2 if they're a pair.
The cycle can be started with ammonia as well. I'm not too familiar with that method, so I'll leave that for someone else to answer.
Hope this helps.