For mine, the new outgoing email option appeared automatically in Apple Mail as an option. No need to "add" another account at all. I did find that on the beta.icloud.com site, go to the Mail page and there's a little gear at the top of the left column. There I could update the "send as" line to look better. Clearly this is in beta as it was glitchy for me, but it finally worked.
FWIW - the new outgoing email option also appeared on my iPhone with no action on my part at all. Certainly didn't "add" any new accounts ... it just worked!!
As I mentioned before, Outlook does not provide me the new outgoing email address yet. I suspect the same may be true for other 3rd party email clients. They'll probably need to do something to make them work. Incoming mail works fine in OL.
Ken