Not a chance Oneeyedhen. Firstly they will be attacked by the hens. Secondly, those that survive will find somewhere warm and safe rather than a draughty cage.
They need their own coop and run until they are laying, then you can better integrate them.
We faced the same problem and I had to build a small coop and run every week for 4 weeks, then two large coops and runs for hens and cockerels.