I've been doing exactly that for 5 years now. I've never had trouble filling spots. In fact, I always have waiting lists. As you said I close all summer, Christmas and March Breaks. At the beginning of the year I start when the teachers go back, obviously...not when the students start and same for the end of the year. In other words I follow the teacher's schedules, not the students, which means I work PD Days.
There are only pros! Well, except for the pay, I suppose, but it's all about priorities. It helps that my husband is a teacher and has gotten me a lot of my clients, but in my ads it's clearly stated and I say that it's perfect for teachers "don't pay, don't lose your place!"
Good luck! Our kids are only get one childhood! Let's spend as much of it as we can with them!