If there is a drone laying queen in the hive you would have to remove her before introducing any eggs ... there's little chance of them raising a supercedure cell with the DLQ still in there. Personally, in that situation, I would despatch the queen and combine the colony with another colony as you are going to have elderly workers by the time a new queen was raised and a predominance of drones ... better to use them somewhere else whilst they are of use rather than risk them not raising a queen, watching dwindling numbers of workers only to find that after weeks you still don't have a viable queen.
Sometimes it's better to just cut your losses.