you can 100% have a cycled tank with carbon. carbon is good for removing things from an aquarium that you dont want. it doesnt absorb bacteria. it can absorb meds, nutrients, chemicals etc. the key thing with carbon is that it does well at absorbing things, but only does so for a short time before it has absorbed all it can. after that it is pretty much an inert substance. it is a handy tool, and it has its time and place for use, beyond being a money maker for filter manufacturers.