Yes, this will work. With any assignment set to File Upload, students can submit from Google Drive or OneDrive if those integrations are enabled. So if the collaboration was created using Google Apps, a student can submit that collaborative document to an Assignment just like any other file in their Google Drive account. And if it's a group assignment, that file is summitted for everyone in the group.
As for the teacher and TA having access, if they Teacher initially created the document under collaborations they should already have access to it. I'm not as certain about a TA but they should see it listed under collaborations and I think can click to access. Keep in mind that when the file is submitted, it's a copy of the collaboration file and submitted exactly as it was when they clicked submit. Accessing the file through Collaborations lets you see the file in it's current state which could have been edited. Viewing it through Collaborations also lets you view the history of the file as capture by Google app or OneDrive. You won't see that history on the submitted version to the assignment.
Hope that helps,
Rick
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