I wouldn't put that much in. Start with 1-2 ounces max. Refill as needed. Kids are skilled enough to use an open cup that young, BUT it takes adult supervision, which isn't always possible in group care.

Personally I would tell the family you will use a straw cup and will provide chances for open cup when you are able to help. Tell them to have the child master the open cup at home for a bit. Inform them that a straw cup can promote motor skill and aids in speech it is not the same as a sippy cup.