Yes.  See Theorem 7 of the paper [A survey on Seifert fibre space conjecture][1] by Jean-Philippe Préaux.  One has to understand the "Seifert spaces modulo $\mathbb{P}$" introduced by Heil and Whitten.  (This is the first time I've had to think about these - life is simpler when we assume orientability!)


  [1]: https://arxiv.org/abs/1202.4142