No. Third party apps are exactly that - third party. They are controlled, owned and operated by developers that aren't Shopify, BigCommerce or QuickBooks Online. We have no permission to access them or read the data they contain.
What about apps that change things on my site Oberlo or Shogun?
Apps that push data from their storage to Shopify or BigCommerce like Oberlo or Shogun are slightly different. Data can be backed up once it arrives on the website because the information is now being stored by Shopify or BigCommerce.
Oberlo creates a product and pushes it to Shopify. This creates a new product in the Shopify > Admin which we can backup and save.
Shogun creates a page using HTML that pushes that code to your BigCommerce theme. This data can now be backed up as we have access to your theme.