Yes, You can work ahead and finish before the last day of class. but keep in mind you are squeezing 18 weeks of a course into a very shortened summer session. Reducing the number of weeks you attend means more work in the other weeks, but many students that are planning on vacations, or sports camps can and do finish early.
Here is what you will do....
1. Complete all of the work at home, that is all quizzes, homework whenever you want, as early as you want. Take multiple exams in person, you can take as many as you you want within the school bell schedule. The only restriction is that you must complete all work by NOON on the last day of class.