It depends on how much he is currently skating and what else he has going on. I like to do weekly privates after the season ends before tryouts and throughout the summer. If the child will put in the extra work, then they can benefit from an extra skate a week. But be careful, who is driving the cart, you or the child? At that age, to prevent overuse injuries and to prevent burnout, it isn't necessary to do more.
There is nothing wrong with playing a lower level of ice hockey. Better to be an average player who develops a true lifelong love for the game than burn them out trying to reach for something the kid doesn't want, imho. You don't have to be the best to do something. Just enjoy it.