The only thing tied into CLvl, is doing the Ancients quests. If you are not a CLvl 20, you can get out of Normal mode, since you won't get the quest for Ancients, and you won't be able to get into Worldstone until you are a 20 and do Ancients again.

The same for being a CLvl 40 in NM, and CLvl 60 in Hell.