I have seen carrots actually sprout some new greenery in my refrigerator.  I don't know how much will sprout but take good care of them and a big 'maybe'.  If you want to plant more seeds, check for the maturity days although they are an in-ground vegetable so they can be left in the garden longer.  BUT, you will have to fence the bed off because whatever ate the original carrots has a taste for them and will come back for more.