My class is set up to have multiple weeks. I'd like to have a copy of the same workshop module in multiple weeks, but will duplicating the module keep the submissions and phases the same from copy to copy?
The "duplicate" feature does not duplicate the user data, so the submissions would not be duplicated. There is a way how to do it, but I don't think it is a wise thing to do. What exactly are you trying to achieve?
In the end, because I want them to self-assess and then peer assess, I'm just going to copy it and let students resubmit a draft each time since I can't have two assessment sessions in the same workshop session. That would be a great addition, Moodle. A Workshop flow that allowed TWO assessments. Or am I missing that function??
Instead of duplicating the workshop, I would just put one workshop in 4 week, and then add a HTML link to it in the other three weeks.
These are two things. As Al correctly pointed out, it is better to keep a single instance of the workshop and just link to it from the other sections. Alternatively, you may need to manually move the workshop from week to week.
Workshop does support iterative / repeated peer-assessment - kind of. You can switch the phase to the assessment one repeatedly as needed. Each iteration can even have different grading strategy selected. For example, you can gather initial feedback via the Comments grading strategy for the first round, let authors submit new versions of submission based on the feedback, and then assess it again with more formal accumulative or rubric strategy. It is an advance feature though and is recommended for teachers familiar with the Workshop workflow and features.