We've fried and baked on the same day of processing. The meat is tougher, but still good IMHO.
We've done this with rangers and quail and will soon do it cornish x.
Not only will it be tough, any cuts you make will look unappealing due to rigor mortis (will appear ragged after the muscles relax.) I'd say chill overnight.
i processed one of my extra roosters and eat him them same night. i put him in a pot of slat water for about 5 hours and ate him that night came out really good! well i thought so.