Is your kid eligible to earn SPG points from the DL crossover program?

They can't get points from hotel stays because to the stay and pay requirement, bu they might be able to earn points from other sources, including restaurant spend.

ADDED: have you looked at the SPG T&C, available online? What happens if you just try to open an account? Does it ask for the person's age or birthdate or otherwise indicate at some step that there's an age restriction?