I would probably say not to bother saving the carbon. There will be a bit of biobugs growing on it but carbon granules are not an ideal growth media for biobugs so your lost will not be huge. If you wanted to save them, you will need to keep them in some tank water with an airstone oxygenating the water and then it still has the question of feeding the bacteria with ammonia. Too much work for little gain. Just put some new carbon in when the treatment cycle is over.
As for the other question, yes, the filter function will not be as effective without the carbon but then again they don't want the carbon to filter out the meds so you can't really have it both ways. Just do a 50% water change after the meds is finished to freshen up the water and insert the carbon again.