You can do that much easier. Export the entourage file to RGE. Now get them backed up to the online storage of your desire.
But one issue will still exist- reading them.
MS has stopped supporting Entourage, as far my knowledge goes. Soon the application will be permanently stopped. It would be better if you switch your mail client to
Outlook/Apple mail as well.
As rest of the mail clients don’t read RGE files, you will also need to convert the mail format as well.
Try out Mail Backup X for the same.
You can export your Entourage emails to RGE format and can import them into this application. Mail Backup X comes with a viewer option that lets you read the emails in RGE format, easily. Moreover, the tool lets you create mail backup at any location of your
choice(online storages included).
As it is not free, you should take the 15-day free trial as well.