IIRC there is some evidence of it, and it's what some of the charters, such as KIPP, which are successful in the inner cities are doing.
I do recall reading somewhere that the kids in lower socioeconomic groups tend to regress more in the summer than other students do. In inner cities, it also tends to keep students out of the toxic street culture more.
Sad to say, there are too many home environments that the kids would be better out of. I've seen plenty of it myself having lived in a welfare town. In those cases, I do think the idea could work.
The problem is, once something is started by the government, no matter how good sounding, it's only a matter of time before it becomes an out of control behemoth.