Parents who engaged with their children are more likely to excel in school and avoid risky behavior?

Assuming the parents are consistent in modeling appropriate behavior and engraining the value of getting an education, Yes, absolutely. Our parents, particularly the same gender parent, are the strongest role models in our formative years. For better or worse. 

The antithesis further proves this point:

It has been proven time and again that the children of abusive parents, or alcoholic parents have a greater frequency of being abusive or alcoholic parents themselves.

Supposedly. Although two things can change that tidy little saying. Freewill and mental illness.

Regardless of the upbringing and environment a person, child or not, has free will and can turn out to be the opposite of all predictions.

Sure. 

One of the primary effects of living in a functional family.

50/50 parents can give everything and have a 99% trouble child and that becomes a destructive adult.

Or 99% give nothing and have a Nobel Prize winner.