Yes, .  because
Children learn to speak through imitation and by that a child must listen first . And an individual could not write anything that makes sense unless he or she undergoes  the reading skill. I guess its always in that order.... 

I think a child must learn to read first before the writing skill. A child can't write a word, a phrase without knowing the  different letters, punctuation marks and etc...
and because of that, reading would always comes first that writing