Not actually a church guy myself, but I assume other people do it.
Yes, taking a day to do nothing is important.
Not necessarily doing "nothing," just not having a set routine, and only doing something if I feel like it. If you make plans involving me on a weekend, that's fine, but please tell me about them by Friday morning, at the absolute latest. That way I can plan my weekend.
This weekend, for example: I am busy all day Saturday with errands, from about 7 a.m. until about 3, then we have a get-together with friends at 5.
So, yes, I technically am free on Sunday, but my plans are to do some get caught up on reading for a couple of hours, do some weeding in the front yard, do the laundry, then go through pictures and such and order things for our upcoming 50/20 party in April. Nothing involving leaving the house. So, technically, it would be accurate to say "I have other plans," even if it's misleading.
(People have a tendency to wait to tell me about plans involving me until five minutes before I need to leave the house for whatever the plans are. I've started cracking down on that: I say, "I'll do it, but, as a warning, I will be quite grumpy about it because I wasn't told about it ahead of time, and I won't be fun to be around.")