Is there a connection between Academic achievement and Behavior?

By no means am I a psychologist nor is what I am about to write scientific or proven. It has been my experience that often there is a correlation between academic achievement and behavior in that the students who tend to cause the most trouble in class are also the ones who are doing poorly academically. We all have our reasons for this and one of the more popular answers is that since they don't understand what is going on in class or it is too hard they tend to tune out and become distracted and bored and the only thing they have left to do is to act out.

However I started reading the book "Switch; How to change things when change is hard" by Chip Heath and Dan Heath. They propose the following which I think could explain the correlation between academics and behavior. They write that, "Self- control is a exhaustible resource....The research shows that we burn self control in a wide variety of situations... trying to focus on simple instructions...."
Based on this I think the correlation is clear, we and especially our students don't have a limitless amount of self control to control our emotions and our behavior. Therefore the more one needs to burn this resource on understand the simple and basic academic questions the less they have for being able to sit in their seat and raise their hands.
What can we do with this. Well first of all I think we need to look at students who don't behave differently and in some cases it is not that they don't want to be respectful or that they are just rude or lazy but rather they have used up their resource of self-control and perhaps that would help us think of them in a different light. Secondly I think it requires us to help those students succeed academically so that they don't use up all of their resources and they can feel success and have a bit of easier time.
This also helps me answer a personal dilemma that I have had. working in a religious school we have a dual program. Half the day is spent on General Studies and the other half on Judaic studies. There are a number of students who are well behaved in their General Studies classes but offer a challenge in their Judaic classes. Granted a number of our Judaic studies teachers come from different cultures and have a different style of teaching but I believe this concept of viewing self control as a resource can also answer this discrepancy. The student uses up less self control on the academic side in his math and history class and therefore has more self- control with regard to his behavior however in the Judaic classes taught mostly in Hebrew they use up more resources on the academic side and therefore less is left for the behavioral side.

As always I appreciate your comments and feedback