Taken literally, this is false. Children voraciously isn't literally an epiphenomenon of their growth. If it were, children would still grow regardless of how little they eat. But in fact, not eating enough when you're a kid stunts your growth.

It is literally true. Notice the tense. It's not an effect of their growth it's an effect of their being something that is growing -- having a hormonal system that is aligned toward increasing size.