Does repeated essay writing help you write them better?

Yes, it helps you a lot. This is why teachers would do several trials to prepare you for doing the real essay because, in this way, you're training and learning how to write in the right way. It is also important to try to write different topics and to learn how to use proper words and sentences.

I recommend you to read a lot (because you will always learn new sentences and words, which you will be able to use in your essays) and develop a good memory for different words. It will help you a lot in the real essay, and you will have higher notes.