Well, I am not a great expert of Russian (even though it's my first language), but I doubt that it's perfectly correct in this context, at least. I think "его" is the better alternative. Why? Because if you really wanted to convey the idea of the childing waiting for himself you would definitely use "ceбя", wouldn't you? If it were a movie where the child were traveling in time and were waiting for himself then it would make sense. So, personally, I think "его" eliminates the ambiguity. If you get rid of the pronoun at all then it's now clear who the child was waiting for.