Activated charcoal/carbon media wouldn't ordinarily be used to contribute to one's biological filtration. I generally only use it for removal of meds, and then take it out.
Removing the carbon and putting it into the filter of your fry tank doesn't sound like a good plan. It could spread disease as you say, and there doesn't seem like much benefit.
What proportion of your filter media is the black stuff? If it's the media that came with the filter, and you also have more white (or whatever) media that also came with the filter, it's probably pretty safe to assume it's carbon.
I'd dump the carbon you have since it's probably not active any more anyway, and buy some more for when you are ready to remove the meds. After a few days remove it again though. Someone else will have to confirm because I wouldn't want to mislead you, but I understand that it will then remain activated until you need to use it again.