Not currently, however we are looking at adding this functionality. Please see Storage Integration With Dropbox, Google Drive, Etc to follow the feature request and vote for it if you would like to see it in a future update.
Can I auto-sync my captured content in a cloud storage service (i.e. Dropbox or Google Drive)?
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"Please see here(...)to see it in a future update: " and link is missing.
Anyhow, would love to get my bubls auto-synced to mobile device and later to cloud when mobile gets into wifi area (some might like only when they are charging)
In mean time , even "batch download to device" and later "batch upload" would be helpful. Now, the only option when selecting multiple files is to "delete" , there should be also "save to app" and "upload" (appropriately).