It's close but if you still have ammonia readings it's not cycled. If you still have Nitrite readings your not cycled and your nitrates need to go thru the roof and down to 10 ppm ( IMO ) before the final stage of cycling which needs fish, this final stage IMO is gonna be the most critical and semingly is the most ignored - the building of friendly denitrifying colonies that change harmful nitrate to harmless nitrogen gas.
If you rush it - obnoxious algae will become your main denitrifyer.
As for carbon - it has it's advantages and disadvantages. It will act as a protien and heavey metal filter. As the protiens stick to the surfaces of carbon much like flytrap strips the protiens still decompose emitting phospates into the water, it can also be a Nitrate bomb as most activated carbon is only active for one month then it releases all it's trapped particals back into the water. The end results can all lead to obnoxious algae blooms.
Protien skimmers and refrigiums are the way to go as they physically remove protiens from the water and QT them in a cup were they rot. A refrigium will house beneficial bacteria and algaes which will eat both phosphates and nitrates as well as other harmful gases, while releasing oxygen back into the water.
I use carbon and an R/O metal/fine partical pad in my w/c tank and top of tank as nothing is living in these tanks and w/c's are every 3 daze the carbon won't generate a bunch of phosphates. Instead it traps heavey metals and organics from my tapwater as well as helping to aid in the removal of chlorine, liquid de-chlorinators are the staple tho. The carbon is changed every 3 weeks. Shortly I'll be adding Phos reactors to all 3 tanks hopefully making the w/c's as friendly as possible. Then I'll ad corals as I have no desire to throw my money away.