From a technical perspective, this would work, as the API does offer the ability to upload and download files. Also, while there are bandwidth limits on shared links, this doesn't apply to authenticated API calls. For example, to upload and download files, respectively:
From a policy perspective though, we can't provide any absolute guarantee of your app's compliance based on this hypothetical description, so you should be sure to review all the guidelines and terms before developing an app:
We love to learn from the educators who use Dropbox. Whether you teach kids, teens, adults or a combination of all three, we want to know what apps and integrations you use with Dropbox to help with teaching. Which of the ones below is your favorite, or most used tool?