Is this possible?

Yes, but you will need to create your own server side service to do it, authorise your own account against that service once and store the Dropbox auth token for later reuse by your clients, and use that token for all actions rather than one generated by each user.

You can't do this solely in Javascript client side, because you would be exposing your entire account via that auth token that you would need to provide - hence the server side component that you need to create, that will handle all actions against the Dropbox API.