Not yet, but we also think that sounds like a great idea! Stay tuned for future updates to the studio. In the meantime, you can use the desktop versions of Google Drive or Dropbox to upload your audio files.
If you're on a Chromebook you can use the "Import file..." option in the studio to import your Google Drive files. If you want to drag and drop files instead (not recommended), you need to access Google Drive from the Files app and not from the Chrome browser (which is where the Google Drive app on a Chromebook takes you.)