NO-- some people will say that conures need a sleep hut but this is a very divided issue and many people report that once they remove dark/shadowy spaces, behavior improves. While you may encounter mixed views on special sleep spaces, a box in the closet is absolutely irresponsible and dangerous.
If you MUST give your conure a space to sleep (which is debatable behaviorally) then it must be in the cage and it should NOT be a snuggle hut or fleece tent. These are responsible for many bird deaths. You could fashion something out of sea-grass, but if you are covering the cage anyway, they will still sleep...
I personally would not have a sleep space for one period, as I have known some very sweet/mellow ones who never had one and did just fine. You can find a lot of info out there from bird trainers etc who are against sleep spaces for conures, but there are also people who insist upon such a setup)
I am not saying that all conures react in a hormonal way to shadowy spaces BUT, it can sometimes be hard to tell hormones from what seems like semi-bratty behavior etc. It is complicated.
(see link above) What you are describing is a serious accident waiting to happen, from suffocation, to escape, to ingestion of foreign objects in the event of escape, to hormones....Plus, cardboard is really questionable for the health of their feet (10 hours of sleep is necessary, so to be in a box like that with poor footing and its own poop is REALLY REALLY BAD)
I'm glad to hear such caution! We keep our birds in their cages overnight. I was just wondering because I thought it was a strange practice based on what I've read. I've been reading about the snuggle huts/tents. We tried one with our little conure before we knew, and luckily he wouldn't have anything to do with it!