I think this really depends on exactly your DS’s attitude. I haven’t had any trouble, I’ll openly tell people I’m atheist if it comes up in conversation (although I certainly had the tact to avoid such topics while at church on Sundays), but I just make sure not to try to say anything that will sound like I’m trying to assert myself as right and them as wrong. Having said that, I’ve had numerous healthy debates on the topic including numerous deep debates with one of my BRs who wants to be a pastor. So you aren’t going to have people condemning you left and right when they find out you’re an atheist. He’ll identify a small number of people that are less tolerant and all I do is just avoid religious topics with them, no problem.
There is a slight Christian “dominance” (not a great choice of words), in that many people will assume you’re Christian sight unseen, and the host family system is only pseudo-official and run by religious entities. These were things that I knew wouldn’t be ideal for me, but I factored that in to my decision and it didn’t way heavily because I decided upfront how I was going to handle myself so it wouldn’t be a real hurdle.
As far as catching up on sleep without church: You could probably do it, most Sundays Cadre/RDC probably won’t spend their free time looking for Rats to bother (they’re presumed all at church anyway), but regardless, he’ll want to get out. The Sunday after hell week all the churches come and give a quick intro and then everyone picks. I picked the only church where the pastor was relatively young and was just wearing a t-shirt. They were very nice people to spend the Sundays with. Even though they ended up having less liberal Christian views than I had gauged, there was still a laid back culture which was nice. Additionally, although I’ve never done this, the Institute Chaplain, who makes a point of being inclusive in terms of accommodating Rats (specifically saying he still wanted to help out agnostics/atheists), has a non-denominational service and then he organized for one of the local inns to be a Rat hangout after his service every Sunday. I just chose the option to get off post right away, so I can’t speak to how that was, but it’s an option.
Really, almost all your BRs are not gonna think twice about what religion you are, you’re all getting screamed at together and hating every waking moment together...That’s going to supersede most differences in opinions.
Sorry for the ramble, if you have more specific questions, let me know.