Although this appears logical, it has not been my experience.
I have 3 teachers kids now. I've normally had a least one parent a teacher always. My client pay for care over summer, March Break, Christmas and they can attend if they want. Sometimes they attend x days a week over summer, sometimes they have some week off and some week here. Sometime they have shorter day in summer with later drop and earlier pick up. I have NEVER had a teacher leave over summer to avoid fees but I explain up front, at interview, that if they want a place here, then they pay year round.
The only time I did have someone leave in mid May and hope to come back in Sept was when one parent in school not a teacher and since they not be honest about that when they joined in Jan., I would not have had them back even if the spot had still been open.