Well, you'd also have to factor in the boy's metabolism in addition to his genes and diet. Even if you are in full control of his environment and nutrition, the boy's metabolism can still fluctuate throughout his lifetime. Something as wishy-washy as height is difficult to accurately calculate within a given time frame. It's possible to find a range, but I don't believe that it's possible to predict an exact height. There are other ways to control it though. If the boy has stunted growth caused by a defect in the pituitary gland (or even malnutrition), he could be given HGH in order to compensate. Nevertheless, that still wouldn't be enough to fully control his height. Actually, what I'm trying to say is, you can't really "calculate" this kind of stuff. Human genetics is lottery, the conditions people reside in change frequently, and trying to predict precise outcomes using numbers is nearly impossible. Nature and nurture will always coincide--they can't run "head-on-head." However, depending on the person, one may dominate over the other. For example, someone with severe autism won't be as greatly impacted by environment as a normal person who is in total control of his or her life (nurture). Instead, the autistic person would be too hindered by the crippling condition (nature).
As for the boy's height, if you theoretically were able to control every aspect that factors into his height, it might be possible to calculate his exact height (don't quote me on this, haha). Unfortunately, this isn't the case. There are countless amounts of these factors, so this would be a highly unrealistic goal. But like I said before--it's still possible to find a range.
I have no concrete answer for your nature vs. nurture discussion. It really varies from person to person. I, however, tend to lean towards nurture being the more significant facet if you're referring to how it affects the average population.
Ahh, sorry if this wasn't much help. It's rather difficult to find solid proof stating that one truly is superior to the other because to be honest, it really can't.