I'm in a high school choir and we just got a new teacher. He is adamant that we don't listen to rehearsal tracks or recordings, because "real musicians don't." Is there merit to this?
It's certainly not true that real musicians don't listen to tracks or recordings... As Mafii says, many excellent musicians don't actually use scores at all. However, it probably is true that most 'real' choristers can read music to an extent.
Is it better to learn a piece by working on rhythms and notes without hearing them?
There are a some advantages to working from sheet music:
If you have good sheet music skills, it allows you to play a piece from the sheet music without having practiced or learned it before at all. That may not always be necessary in your situation, but it does mean that your teacher is able to introduce material to the class without having to have you listen to it first. The score is also a useful aid to memory even if you have learned a piece somewhat 'roughly'.
in a complex piece, it's going to be much easier for most people to pick out their line from a score than by ear.
In rehearsal, it's much easier for the choirmaster to be able to say 'Ok, let's start from bar 47' and have everyone able to pick up from there, than try to describe things in any other way. It's also good to be able to annotate a score with instructions. It's this practical way of 'working from the score' that your choirmaster probably needs you to be able to do.
Of course, there are some advantages to working with recordings too - it means you don't have to learn to read the score, most people (even proficient readers) can probably get the piece into their "mind's ear" more quickly from a recording, and a recording of a good performance might reveal stylistic subtleties and inflections that aren't obvious from a score - not to mention that you can 'study' a recording while jogging, doing homework, etc.
He likes sight reading with as little help as possible. It is very slow work, even though we're supposed to be the top choir in school, making our performances lackluster.
It sounds to me like you need to meet each other half way. Big ensembles do usually work from scores for good reason, and members of most choirs should probably aim to improve their reading skills. However, if some of the members of your choir don't have sufficient reading skills, perhaps your teacher should compromise a little on the "as little help as possible" bit.