It's possible to embed a feature to upload a file to Box from within a Qualtrics survey.

1. Follow Box's instructions to set up a Box File Request.
2. In those same instructions, look for Embedding File Request into an existing Web page. That section tells how to get the HTML code you'll insert into your Qualtrics survey.
3. Once you have the HTML code, go to your Qualtrics survey.
4. Create a question type of Text/Graphic. 
5. Click where it says Click to write the question text.
6. Select the Rich Content Editor tab.
7. Click the icon that is a rectangle with <> in it (Source).
8. Paste the code provided by Box.

It's possible that when previewing the question, the Box part will be in a window too small for it, in which case the the question's scroll bars would have to be used to see the submit button that uploads the file. If this is the case, some people taking the survey might not see the upload button and instead click the button to advance the survey. To address this, go into the HTML code and adjusted the height to 900 and the width to 750 or other values larger than were originally there. When the dimensions are correct, the frame for the file upload should be big enough to see the Submit button automatically.