I always start the skimmer immediately. I had uncured live rock also and it works fine. It won't hurt your cycle or anything. A lot of lfs run a skimmer in their live rock bins. There will be some die off, thus starting the cycle. The skimmer can't pull out the decomposing matter actually in the rock and that is plenty of food for the bacteria.
I do water changes during the curing/cycling also (some people dont). I still get good spikes during cycling and dont have to deal with ridiculously high nitrates when done. I believe that the water changes also help beneficial hitchhikers survive (another controversy- live rock vs dead rock, cool stuff vs nuisance). I got a free leather, button polyp, calcarous macroalgae, porites, limpets, chitons and even a lime green montipora.