If you keep an intense eye & consistently double or triple up kids on the mushrooms, and pause when you're away (even for a short time), a village of 15 to 17 is possible, but anything higher than that and you'll start running out of food.
Heck . . . you can sustain even more than that, if you rain-dance a lot. You can sustain a healthy village without ever preparing the comb or the trees, if you have no problem unpausing the game only when you're at the machine, scanning fiercely for mushrooms.( I'd say a village of 10-12 villagers on mushrooms alone isn't inattainable, but you'll never be able to rain-dance for mushrooms if you don't farm. I miss the farm. Even if it was the only source of food, it gave your farmers 'practice' tasks.
All of my numbers are for the sake of planning and predicting a village's food supply during the time you're away; therefore mushrooms are no part of my assumptions.