most people dont use carbon unless removing medications from the water as its good for this. it will also remove tannins from wood that stains the water brown. dont worry about not having it in as it will not do any harm. the only thing is if its been in the filter for a long period then you may have colonies of beneficial bacteria you need in the filter to remove ammonia and nitrite so just check the water for a few days, although it shouldnt be too big a piece of media to be removed leaving you plenty left. anything below 20-30% of media removed is fine depending on stocking
if your treating for disease then i wouldnt as the new fish may get the same trouble and also bring in new ones....
unless you have a quarentine tank to put the new fish in which is really advised so no nasties are introduced to your main tank and if needed treatment can be given just to the new fish and not the others that may be fine. if you dont have a qt then i wouldnt add any new fish etc until at least a week or two after the dosing of meds are complete and the tank is a happy place again. dont forget to put some carbon back in to remove any meds in the water before adding new fish too, if the carbon removed has been in the filter a while i would get a new cartridge as apparently it doesnt last too long and becomes useless. people tend to give various periods of time that carbon is usefull for but as its relativly cheap i would get a new one wash it before putting it in the filter to remove the fine dust etc. also a good water change may help to rid the tank or any meds remaining and go give the fish a boost 
