How the US Dept of Education define a school year for purposes of Pell Grant eligibility?
Yes and no.

You can only use your Pell grant money for summer classes if you've already been enrolled in classes  the previous year:

To be eligible for using this federal aid for their summer courses, students must have completed 24 credit hours toward their degree programs during the prior fall and spring semesters and have received passing grades, and they must enroll in at least 6 hours of courses during the summer.

So if you want to attend summer classes in 2016, you had to have 24 credit hours of schoolwork done at the same institution during the 2015-2016 academic year.

Campus Explorer, Pell grant can be Used for summer college courses, starting in summer 2010.