Would you use carbon during cycling of a new tank?

I don't see where you would have any issues. Many of the organic compounds that will be released during setup, cycling, maturation, etc. will be removed by carbon. It isn't really as hard on trace elements as many would believe, too, since it primarily only targets those that complex with organic molecules (so unless you like your copper...). Sounds like a win-win situation to me. FWIW, I use it 24/7 from day 1 and in every tank I've ever owned. I replace it about every 2-3 weeks.