You do not need any rock to contribute to an esatblished or for assisitng a nitrogen cycle if your tank is already cycled. Most reef fish like haveing hiding places so both would be beneficial for that reason. Reef ecosystems are very complex and a lot more is needed than just bacteria for the nitrogen cycle including cryptic sponges that are essential recyclers for the various DOC compounds generated. Maricultured or wild live rock is the best source for those. See Aquabiomics article here
Live rock is good to introduce beneficial microorganisms, and add to the tank's biodiversity. Rock in general is important in a reef tank, for hiding places and spots for bacteria to live. If your tank is already cycled, you don't need live rock to add more bacteria, but it's good to add all the helpful little critters. A couple pounds of really nice live rock (not just stuff that's been in a bin, you want ocean rock) is a great addition to any aquarium that wasn't started with the nice live rock in the first place.
Entirely depends on how you cycled the tank and what was in it at the time.
Cycling a tank is simply a term for colonising bacteria on surfaces - if you have no rock when it cycled, what did you have to ensure the bacteria lived on? Very, very little is in the water column.
I’d fear the tank is not already cycled without rock of any sort to be honest.
what makes you say the tank is already cycled if it’s rockless?