I need to upload a student's document (Word doc) to the Moodle workshop but I don't see a way to manually add it for them. Is there a way to add a document into the workshop for the student?
Yes there is.
At the Editing Workshop form (when creating a new activity or editing an existing one), put a link to the file into the appropriate editor field. Depending on when (in which phase) you want to provide the file, embed it into the Description, Instructions for submission, Instructions for assessment or Conclusion field.
In the default Atto editor, enter some text such as "Download the submission template". Select it and then click the "Link" button in the editor toolbar. Then "Browse repositories" > "Upload a file" and pick your document to be uploaded.
Ah sorry, my misunderstanding. If the workshop is still in the submission phase, you should be able to use the "Log in as" feature maybe? I don't think there is another way. If the submission phase is over, you can still have students involved for peer-assessment.