This is possible. You would have to have start by listing files/folders in the root folder and then loop over the returned array. While looping, files can be copied into blob storage and folders could recursively call the same logic app.
Note that to recursively call the same logic app, you will have to use the HTTP Action instead of the Logic App Action which doesn't support recursively triggering the logic app.
Also, make note of individual connector limits for files size for which you will have to enable chunking.