Rich9876,
Glad you're back! Thanks for testing this out because you were able to verify that you'd need two-factor authentication code.
We were able to dig into this further. We've found this guide: What is Hide My Email? It gives clearer information "You can read and respond directly to emails sent to these addresses ", and it doesn't look like you can initiate them.
If you wanted to do this, maybe setting up an iCloud Mail Alias might be a better solution for you. Check this out: Add and manage email aliases for iCloud Mail on iCloud.com. It explains this in better detail and shows you how to set up an email alias using iCloud.com. By doing this, it should allow you to see this when you select "From" when sending emails.
Cheers!