Over a third of the students at my middle school were in band, and lots of them had academic problems. By eighth grade, they were all ok enough at reading music to get through multi-page pieces together.
Only a few of us could have told you what a major third or the circle of fifths was, but frankly, even that meager level of theory was useless for the immediate task of playing the same note at the same time as all the other second clarinets.
Band players don't really learn to read music as such, they learn to read finger/hand positions. This is much easier. Sheet music is really a lot like instrument-independent tabulature, but it's a bad for singing or any instrument with lots of positions or where you play many notes at once (e.g. piano)
