Well, O'DAY did offer cushions for the cuddy as an option on the DS II for several years, so it is "possible"! Sleeping in the DS (II or III) Cuddy would be one small step up from a small tent in that the "roof" would never collapse during the night! You would definitely need a vent (preferably powered/fan) located forward to create airflow through the space and adequate screening to keep out the "no-see-ums"! Crawling into bed would be an accurate way to describe the experience. Where to stow gear (clothing, food, normal boat gear ,etc.) could be interesting, as you will not want it taking up room with you in the cuddy. Finally, dealing with the "call of nature" is not going to be a very private task on a Day Sailer, and no place for a porta-potty!
I'd suggest making a removeable plywood platform to bridge the cockpit seats as your sleeping platform, with a tent over the boom (could use PVC pipe "hoops" to create more room under the boom tent. Consult books on small boat camping for ideas. I have seen some interesting tents st up on O'DAY Day Sailers of various vintages that look promising. It CAN be done, but will take some serious planning! I had a few pictures of interesting boom tent variations that I had saved, see below.