That's an interesting hypothesis - however, I am not aware of any evidence that this is the case. Importantly, there can be a lot of difference between cellular access to energy, like ATP, and the perception of "energy" or liveliness.
Here is a paper that actually suggests the opposite: that ADHD could be caused by a neuronal energy deficiency because of differences in astrocyte responses to catecholamines (astrocytes are non-neuronal cells in the brain that, among other functions, regulate metabolism in the brain including access to glucose). Importantly, though, this remains just a hypothesis, not a well-established theory.
ADHD is thought to impact the parts of the brain that are important for attentional control, inhibiting responses, and motivation. Based on that perspective, an alternative explanation for the symptoms you describe is that a sensation occurs that doesn't really require a behavorial response, and for a neurotypical individual this sensation is quickly suppressed (attentional control by not focusing on this sensation, inhibiting your response to shake your leg) without any real conscious effort. Instead, with ADHD, it is difficult to direct focus away from that sensation and mental resources need to be directed towards trying to hold still. The relief from moving around comes from letting the activity progress and not trying to suppress it any more, not because there was a literal excess of energy in the sense of ATP.
Barkley, R. A. (1997). Behavioral inhibition, sustained attention, and executive functions: constructing a unifying theory of ADHD. Psychological bulletin, 121(1), 65.
Todd, R. D., & Botteron, K. N. (2001). Is attention-deficit/hyperactivity disorder an energy deficiency syndrome?. Biological Psychiatry, 50(3), 151-158.