Personally, I'd say it counts. It is recommended that we only have one serving of juice a day though-- juice lacks some of the fiber & other nutrients that whole fruit has. This article is healthy beverage guidelines: www.sparkpeople.com/resource/nutrition_art
The USDA website talks about a serving of juice being 3/4 of a cup, so the school juices might be a bit *skimpy* on a serving but then presumably they're sized for kids anyway.
So drinking one would be okay, but drinking a whole bunch of them each day, to replace soda or coffee.... you'd be better off drinking water.