If you have a set day each week, it can be difficult, but it IS doable. The AT would be MUCH easier to achieve this sort of schedule since there are more town stops. Circuit Rider, a minister I knew from my 99 thru-hike always arranged either a Sunday church visit or a Wednesday night service each week, sometimes both.
From a technical viewpoint, it is doable if you plan carefully. When you factor in town stops, you will likely wind up only slightly "in the hole" by observing a sabbath. Many hikers manage a town stop a week in many parts of the AT and PCT. You may have to pour on some mileage or lolligag in certain sections, but it is often doable. If not, find a campsite near a truly stunning vista or comfortable water source and enjoy yourself.
As for the trail being "work", my experience says you have the right approach. It really does become a routine where you "earn" miles instead of money. Those who said, "I'm only out here as long as it's fun," rarely completed a thru-hike. You need a deeper drive to keep you going when times are tough. Of course, it's nice to have a "job" you love most of the time.