No! The reason there are Round Breaks and Bye Days is to allow you to take a rest from grinding in the Altador Cup. Playing during these days are considered "practice rounds". All Prize Point amounts are calculated and balanced based on only playing on actual game days (so not including the breaks or bye days) to make sure they can be earned without interfering with your lives or causing strain or injury through excessive grinding. Of course, you'll still have to work hard to get all the prizes, but you should be able to earn more by grinding less.
You'll also be able to earn additional points by completing Achievements!