I have zero qualifications here, but I'm pretty sure the answer would be yes. The depression occurs due to the childs life and how they perceive it, ergo, the world is against them, no one likes them, they believe that they have social issues etc.
It would be difficult to detect though, especially if the child is good at hiding emotions and/or is an introvert.
Medicine is almost never the only cure.
Thanks for your question! :)