To be honest, I have tried and used both live rock in before and after water but I don't think either helped me a lot - it's really if you have multiple pieces you want to stick together outside the tank that adding to a dry tank can help.
Have you tested pumps/heaters/pipework in the sump/tank wet yet? While only half full of saltwater, it would be easier to see leaks and fix; saltwater is too expensive to waste

.
Personally, I would leave the UV and Calc reactor out of any plan right now. As above, skimmer, heater, live rock, water, sand and lights (so you can see stuff in the rock!) would be my priority (I too can recommend temp controllers with titanium heaters and auto top-ups but weigh up costs while you cycle the tank). Don't rush the cycling process though, bacteria is a sloooowww worker - you can speed it up by using live sand or one of the bottled products, off the shelf, to do a bit of this but waiting is a much better way IMHO.