We are planning to implement a feature to let customers browse their images in their own google drive or dropbox accounts (within our app), and select ones they wanna use in our
I ran into your question during my search of finding a way to transfer data from G-drive to Google Cloud Storage. Since they are both under Google umbrella, so I guess they should be able to seamlessly upload/download. So far in my search, without programming, the answer is NO.
I don't have a exactly solution for your question, because it really depend on how much data you have and how often of the uploading/downloading. Unfortunately, there is not straight shot (even for the Gdrive!). But maybe thinking of trying the RESTful API calling to Google and make the connection with Dropbox API. Hoping this could help.